Mr Brown said that the switch to the Alternative Vote system could be part of a "new politics" which would restore public trust in Westminster in the wake of last year's expenses scandal.
In a wide-ranging package of planned reforms, he also confirmed that a draft Bill to create a democratically accountable House of Lords will be published within the next few weeks.
And he gave his backing to parliamentary reforms to give MPs more power over the running of the Commons, new avenues for public petitions to be submitted for debate in the House and the swifter release of official documents under Freedom of Information laws.
As part of moves towards the creation of a written constitution by the 800th anniversary of Magna Carta in 2015, Mr Brown announced that he had asked Cabinet Secretary Sir Gus O'Donnell to codify the unwritten rules governing the operation of central government.
A separate working group will also identify the principles behind the constitutional relations between the state and the individual.
Amendments being tabled today to the Constitutional Reform and Governance Bill are understood to provide for MPs to vote on whether a referendum should be held on the use of the Alternative Vote in Westminster elections.
It is thought that the Commons will vote on the issue before it rises for its half-term break next Wednesday, and Mr Brown's spokesman this morning insisted that enough parliamentary time remains for it to reach the statute book ahead of the election, which must take place by June 3.
Mr Brown today confirmed that he will campaign for a move to AV - under which voters rank candidates in numerical order, rather than simply placing an X on the ballot paper - in the referendum, which he said should be held by October 2011.
In a speech to the Institute for Public Policy Research in London, Mr Brown said the public had been "rightly outraged" by the expenses scandal, and change was needed to restore trust in politics.
While Labour had already taken great steps through devolution, the introduction of freedom of information legislation, the creation of an independent Bank of England and a Supreme Court and the removal of most hereditary peers from the Lords, Mr Brown said he was "frustrated" that the process had not gone further.
"While this Government's record is one of real change, the changes we have made are not nearly enough to deliver the new politics which I want to see and which we need to secure for the benefit of the British people," he said.
Now was the time for "a radical, modern, open and democratic agenda to change the way our country governs itself", he said.
Mr Brown said that Britain faces a choice between "whether we advance towards a new politics, where individuals have more say and more control over their lives, or whether - by doing nothing or by design - we retreat into a discredited old politics, leaving power concentrated in the hands of the old elites".
Confirming plans for a draft Bill for a "democratically accountable" House of Lords, Mr Brown said that "a modern democracy cannot tolerate power to initiate and revise legislation being held forever by those without a mandate for the people".
And he said there was "simply no space" for a hereditary principle in Parliament, which would be removed by legislation to prevent the appointment of new hereditary peers.
Mr Brown confirmed that the Government was backing the recommendations of the Wright Committee on parliamentary reform to allow parties to elect their own members of the select committees which hold Government departments to account and for committee chairs to be elected by a ballot of the whole House.
And he restated his support for a new power for voters to recall MPs in cases of financial impropriety.
Spelling out the case for a move to AV, Mr Brown said it would maintain the benefit of a close constituency link for MPs, but also offer voters increased choice and ensure that all those elected to Parliament have the support of more than half of their constituents.
"It... offers voters increased choice with the chance to express preferences for as many of the candidates as they wish. It means that each elected MP will have the chance to be elected with much broader support from their constituency, not just those who picked them as their first choice," he said.
"In short it offers a system where the British people can, if they so choose, be more confident that their MP truly represents them, while at the same time remaining directly accountable to them."
Mr Brown made clear that there was no question of first-past-the-post being dumped for this year's general election.
His backing for AV was dismissed as a "deathbed conversion" to electoral reform by the Liberal Democrats, who support the more proportional Single Transferable Vote system.
And Conservatives accused the Prime Minister of wanting to "fiddle the electoral system" in order to cling on to power.
Mr Brown said: "The parliamentary expenses scandal scarred our democracy, battered the reputation of our Parliament and so profoundly breached the bond of trust between the people and those elected to serve them that it called into question the very legitimacy of Parliament and of our political system as a whole...
"The urgent imperative for politicians on all sides is to do everything we can to connect with the people.
"The current movement for constitutional change and new politics is of historic importance. It signals the demand for a decisive shift in the balance of power in Britain, a long-overdue transfer of sovereignty from those who govern to those who are governed, from the old outdated sovereignty to a modern popular sovereignty, not just tidying up our constitution but transforming it."
Labour backbencher Tom Harris, an opponent of electoral reform, claimed a majority of Labour MPs wanted to stick with first-past-the-post voting.
But he said, if there was a whipped vote next week, then the "vast majority" of Labour MPs would probably support the Government.
"Because, for a lot of people who support first-past-the-post, the alternative vote is the least worst alternative," Mr Harris said.
"But I don't think anyone is enthusiastic about this and a lot of people will be supporting the Government through gritted teeth."
Speaking to BBC Radio 4's The World At One, he added that it was "utter nonsense" to think that constitutional reform was any kind of response to the expenses scandal.
"It's a complete myth to suggest that the answer to the expenses scandal should be changing the electoral system. It's just Monty Python politics," he said.
Liberal Democrat frontbencher Chris Huhne indicated that his colleagues would probably also back Mr Brown's proposal.
He described the alternative vote as a "baby step" and said his party would try to amend the Government's proposal so that a fully proportional system was considered.
"We will make the case, clearly that's what we would prefer," he said.
"In this particular case, I suspect we will end of supporting it grudgingly because it's a step in the right direction but I don't think it's what the country fully needs."
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