A union chief hailed Ed Miliband's election as Labour leader today as a "clear sign that the party wants change".
Tony Woodley, joint leader of Unite, called on the party to unite behind the new leadership.
He said: "We welcome Ed's victory - this is a fantastic achievement for him and for the policies he has been promoting.
"His victory, coming from nowhere a few months ago, is a clear sign that the party wants change, to move on from New Labour and reconnect with working people.
"Ed has won by hitting the issues people care about - stopping the assassination of public services, fighting for a living wage, standing up for manufacturing, a better future for young people.
"Now the party must unite behind its new leadership and take the fight to the Tories.
"Under Ed, Labour can give a clear lead in opposing that threaten the very fabric of our society. That is what the party expects - a move on from the factionalism which weakened it in government."
Left-wing Labour MP John McDonnell (Hayes and Harlington) called on the new Labour leader to hit the deck running by pledging to lead the resistance to the Government's cuts in public services and set a radical new agenda to tackle the deficit, including controlling the banks and bonuses, cracking down on tax evasion, creating jobs by investing in renewable energy, transport and housing, scrapping Trident, and withdrawing from Afghanistan.
Former Labour cabinet minister David Blunkett said the new leader and his brother had to form a united front.
He said: "We've never seen anything quite like what we've had, with two brothers neck and neck.
"These are brothers. They're blood brothers. They can't afford to fall out in the way we had with Tony and Gordon, and neither can we."
He said he believed Ed Miliband had won the election in the last few weeks.
"If the election had been at the end of July, I think David would have won," added Mr Blunkett. "That takes courage and it takes tenacity."
Ed Miliband is the eighth Labour leader that Mr Blunkett has seen in his time in the party.
He added: "Only two of them so far have won elections. Ed's got to be the third."
Mr Blunkett praised the new Labour leader, saying: "He's articulate, he's able, he's energetic, he's got the organisation to be able to sustain that.
"Now we've got to reach through to the people."
John Sauven, executive director of Greenpeace UK, said: "We have high hopes that the man who brought an end to the era of coal-fired power stations with unlimited emissions will be the right man to hold Cameron's 'greenest Government ever' to their promises."
Scottish Labour leader Iain Gray said: "Ed Miliband will be a great asset to not just Labour but the country.
"Victory in the Scottish elections next year can be the platform for Ed Miliband to be the next Labour prime minister of Britain, and soon.
"Now we will have a strong Labour opposition exposing the folly of the coalition cuts just as Labour at Holyrood has exposed Alex Salmond and the SNP's legacy of failure."
Adam Marshall, of the British Chambers of Commerce, said: "We urge Ed Miliband to make reconnecting with business, both locally and nationally, a key priority of his early months in office.
"Economic recovery depends on improving business confidence, and making it easier - not harder - for companies to take new people on."
Liberal Democrat deputy leader Simon Hughes said: "I want warmly to congratulate Ed Miliband on becoming the new Labour leader.
"It is good to hear that he intends to practise a new politics of working across party boundaries in the national interest.
"The country has a tough time ahead and it will be vital that he wakes up to the challenge that Britain faces. As leader he must recognise that his party can no longer remain head-in-the-sand deficit-deniers.
"Much has to be done. We have to restore Britain's reputation around the world, which was broken by a foreign policy under Tony Blair. And we must restore our economy, broken by the boom and bust of Gordon Brown.
"I also hope he will work to help clean up politics, end vested interests and, as a leader elected by the alternative vote, I call on him to support the cross-party campaign for a fairer voting system from now until the referendum next May."
Nicola Sturgeon, deputy leader of the SNP, said: "Ed Miliband's first test will be next May's Scottish elections when voters will face a choice between an experienced SNP team that has Scotland at its heart and a Labour Party that is Westminster-focused, out of ideas and out of touch.
"The SNP is looking forward to that contest."
Unison general secretary Dave Prentis said: "Congratulations to Ed on being elected leader of the Labour Party.
"Unison backed Ed Miliband because of the way he listened and understood the needs of ordinary working people. We look forward to working together to challenge the coalition Government and its regressive cuts agenda.
"Under Ed's leadership, Labour must offer an alternative economic strategy, promoting growth and recovery, together with fairness. This means protecting the poor, the sick and the vulnerable from the fall-out of this banker's recession.
"Protecting public services, and defending them against sweeping privatisation, must be central to this vision of a fairer society.
"As a priority, Ed must reconnect with Labour's lost voters, including public sector workers, many of whom have been turned off in the past because they believed that Labour had deserted them."
Les Bayliss, Unite's assistant general secretary, said: "The election of Ed Miliband provides the whole movement with the opportunity to wipe the slate clean - a chance to bury the squabbles of the recent past and to build on the promising opinion polls that put Labour level with the Tories.
"Labour needs to listen to union members just as we do. The priorities of working men and women must form the core of all our policies as we go forward.
"It's important that we are able to display a united front when we present an alternative economic programme to the slash and burn approach of the coalition. If we fail to take this chance then we will be betraying a whole generation to the ravages of the Tories and their sidekicks."
Former Labour Cabinet minister Tessa Jowell told Sky News: "I was supporting David very strongly, so obviously personally I feel disappointment.
"But the point is that it has been a long campaign, all the candidates have engaged with a huge number of Labour Party members, and the important thing is, now, everybody in the hall, whoever they voted for, will rally behind Ed as the new leader of the Labour Party."
Peter Hain, another former Labour Cabinet minister, said: "I'm delighted, but you saw the narrowness of the vote. These are two outstanding leaders for a new generation in politics, and they are going to play a big role in the future.
"I think we are now in the position to start to win back the five million voters that we have lost since the last General Election."
Former secretary of state for Scotland Jim Murphy said: "This is day one of Labour's fightback against the Tories."
The East Renfrewshire MP said: "Ed has a great energy and passion and I believe we can win the next election.
"Being Labour leader is a huge responsibility and he is carrying on the flame of generations past, so that the next generation does not have to grow up knowing only a Tory Government.
"Ed has a huge knowledge of Scotland and won the backing of the most number of MSPs. I know he will help the Scottish elections next May in any and every way, and will be an asset to Scotland in the great fight against the Tories and Lib Dems."
But Scottish Tory leader Annabel Goldie said: "If Labour is to regain any credibility, it needs to accept its culpability over the legacy of debt it left our country.
"Whilst Labour north and south of the border is an ideas-free zone, the Conservatives will grapple with the tough decisions needed to take our country forward."
Alan Ritchie, general secretary of building workers' union Ucatt, one of the unions whose support for Ed Miliband proved crucial, said: "Ed Miliband has the vision and the drive to lead Labour to victory at the next general election.
"His belief and commitment that exploitation in the workplace must be eradicated, demonstrated by his support for the living wage, will help Labour reconnect with many of its natural supporters who did not vote for the party in May's General Election."
Friends of the Earth's executive director, Andy Atkins, said: "Congratulations to Ed Miliband on winning the Labour leadership - he is the greenest leader of the party to date.
"Ed Miliband genuinely understands that tackling global warming is essential and he was a key figure in the development and passing of the UK's ground-breaking Climate Change Act, originally proposed by Friends of the Earth.
"Developing a low-carbon economy and protecting the planet's natural diversity must be at the core of his leadership and, with a new Energy Bill on the way, he will have an early chance to establish Labour as a constructive opposition on climate change, ready to challenge the coalition to implement ambitious carbon-cutting policies."
Shadow Chancellor Alistair Darling said: "Ed knows that to win back the trust of the British people we have to chime with the electorate.
"He spoke a lot of common sense in his acceptance speech and he knows the economic recovery is not derailed. We are at a critical point in getting the deficit down but the Government is risking losing tens of thousands of jobs."
Labour MP and former union leader Jack Dromey, who is married to Ms Harman, said: "With Ed at the helm we have a great leader who will lead a great national movement to defeat the coalition Government.
"We now have the chance for a popular progressive politics with a leader of integrity."
Ed Miliband's campaign agent, Sadiq Khan, told BBC News it had been an "exciting campaign" over the past four and a half months.
But he added: "Whoever would have won, we would have seen the Labour family coming behind the winner, and I'm pleased it was Ed Miliband."
He was allowed in the room when the result was announced to the candidates shortly before the conference was addressed.
Mr Khan said "the tension was unbelievable" in the moments before Mr Miliband learned he had won the vote and that it was "really emotional" for all concerned.
He said Ed Miliband had "excited people he met along the campaign trail", and added: "He's learned lessons from Labour's defeat in May. We need to learn those lessons by changing our policy, by changing our way of politics."
Labour MP Yvette Cooper revealed that she had only cast a vote for her husband, Ed Balls, and had not used her second, third or fourth votes.
Also speaking on the BBC, she said of the result: "Both David and Ed got very strong support in every section. What will matter now is that the party will unite. I think Ed will be able to unite the party in order to do that."
Former Labour leader Neil Kinnock told the programme he had offered Ed Miliband advice several weeks ago.
He said: "I told him 'Don't be Leader of the Opposition for long, because that's pure purgatory - the best way out of that is to get elected'."
Liberal Democrat Secretary of State for Scotland Michael Moore said: "I congratulate Ed Miliband on his win.
"I hope that he will use his new job to bring forward constructive suggestions to reduce the record deficit that we inherited from the Labour government."
John Prescott took to his Twitter page to congratulate the new Labour Party leader, writing in a message to Ed Miliband: "Well done. Now let's all unite together and stick it to the coalition."
He had earlier wished all the candidates luck and vowed: "We'll all unite behind the new leader."