Ms Rudd will replace Esther McVey, who quit on Thursday in protest at Ms May’s Brexit deal.
The former home secretary was forced to resign in April over the Windrush scandal but will return to the cabinet after just six and a half months.
The decision prompted immediate criticism from opposition parties, who suggested Ms Rudd’s role in the fiasco should disqualify her from a top government job.
One of her most daunting tasks as work and pensions secretary will be overseeing the roll-out of the controversial universal credit policy, which has been heavily criticised from across the political spectrum.
Ms Rudd said it had "transformed lives" and she pledged to "iron out" problems with the new benefit system - which has been accused of leaving vulnerable people destitute.
In an interview with broadcasters on, Ms Rudd said as a one-nation Tory she wanted to "make sure that we really do help everybody across the country".
Asked whether responsibility for Universal Credit was a "poisoned chalice", she replied: "I have seen Universal Credit do some fantastic things. In my constituency in Hastings and Rye it really has transformed lives. But I also recognise that there have been some issues with it, some problems with it.
"I see it very much as my job, my role, to make sure that I try to iron out those difficulties so it becomes a force wholly for good."
Her appointment came on the day a United Nations envoy warned Universal Credit waiting times have "plunged people into misery and despair".
Mr Barclay, a little-known health minister, will take over as Brexit secretary from Dominic Raab, who also resigned this week in opposition to the government’s proposed withdrawal agreement.
The role had initially been offered to Michael Gove but he is understood to have turned it down in order to continue as environment minister.
The appointments came as Ms May battled to cling onto her job and face down a mounting leadership challenge against her.
More than 20 Conservative MPs announced they had sent in letters calling for a vote of no confidence in her, while others are understood to have done so privately.
Brexiteer ringleaders hoping to oust Ms May claimed they were on the verge of securing the 48 letters needed to trigger a vote.
Confirming Ms Rudd’s return to government Ms May’s spokesman said: “She is a very experienced secretary of state who has worked across a number of departments. There is really important work to do at the DWP implementing the universal credit programme. The prime minister is confident she will do an excellent job.”
Asked about Ms Rudd’s handling of the Windrush saga, No 10 said a report into the fiasco had concluded that Ms Rudd had been let down by Home Office officials.
But Labour criticised the appointment. Jon Trickett, shadow minister for the Cabinet Office, said: “After enforcing Theresa May’s hostile environment in the Home Office, Amber Rudd will now be in charge of the DWP’s hostile environment for disabled people and the poorest in society.
“With universal credit in absolute shambles, appointing a disgraced former minister who was only recently forced to resign for her role in another scandal is a desperate choice by a weak prime minister.”
No 10 said Ms May believed Mr Barclay would do a “first-class job” as Brexit secretary.
Ms May’s spokesman said: “He has experience across government, in the whips office, as economic secretary at the Treasury, and also at the Department of Health and Social Care.
“The prime minister has a good, strong relationship with all her ministers and she thinks he will do a first-class job.”
The spokesman said the prime minister will take personal control of all remaining negotiations with the EU, while Mr Barclay will be tasked with overseeing domestic preparations for Brexit.
Staunch Remainer Stephen Hammond will replace Mr Barclay as a health minister, thus reducing the tally of MPs likely to vote against Ms May’s Brexit deal and in favour of a fresh referendum.
Meanwhile Brexiteer Kwasi Kwarteng will move from the Treasury to replace former Brexit minister Suella Braverman, who also resigned this week.
And Weston-super-Mare MP John Penrose will move to the Northern Ireland Office to replace Shailesh Vara.
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