Phil Woolas has been named as the new immigration minister in Gordon Brown's government reshuffle.
Mr Woolas moves from the environment department where he was responsible for climate change and energy policies.
Sadiq Khan MP has a new job in the communities and local government department - but Parmjit Dhanda MP is believed to have lost his role there.
Other expected moves include left-wing MP Jon Trickett as parliamentary private secretary to the PM.
BBC's political correspondent Jo Coburn said: "That will go some way in placating those on the left of the party and counterbalance Peter Mandelson's appointment."
The Mail on Sunday has also reported that Chris Bryant, who is said to have helped the campaign which pushed Tony Blair to announce his retirement date, will be rewarded with the post of deputy to Leader of the Commons Harriet Harman.
The paper also claimed that Barbara Follett will become culture minister, replacing Margaret Hodge, who was reported to be seeking compassionate leave to look after her ill husband.
Mr Woolas told the Sunday Times he felt immigration was the second biggest problem facing the population and he would "toughen" up current legislation on the issue.
The MP for Oldham East and Saddleworth was at the centre of controversy earlier this year when he raised concerns that the practice of first-cousin marriage in Britain's Pakistani community was leading to high levels of birth defects.
The Mail on Sunday said that the Muslim Public Affairs Committee has already announced that they are concerned about the appointment.
Mr Khan told BBC News Mr Brown rang him to break the news.
He said: "I'm very pleased. It is a pleasure for me to join the communities and local government team."
"He rang me up last night...he likes to do these things himself because he's our leader."
In another change, Shahid Malik has become justice minister.
The Dewsbury MP said he hoped to make Britain "a more just society" in his new role as a minister in the Department for Justice. But Mr Mandelson's return to the cabinet has dominated the reshuffle debate.
Mr Mandelson's appointment as business secretary has not been welcomed by some backbenchers on Labour's left.
And at least one member of the cabinet is believed to have tried to prevent his return at the last minute.
Transport Minister Tom Harris lost his job.
A message published on Mr Harris's website said he was told the news by the prime minister in a phonecall to his Glasgow home on Friday evening.
"Obviously I'm disappointed; I really enjoyed being a minister, particularly in the Department for Transport," Mr Harris said on his website.
"But I was always realistic - ministerial jobs come and go, but the role of an MP is more important than any other. And of course I will continue to support the government from the backbenches."
Mr Mandelson, an EU trade commissioner since 2004, said he was surprised but "proud" when the announcement was made on Friday.
Mr Mandelson twice resigned from cabinet posts under Tony Blair's leadership - once over a loan from ministerial colleague Geoffrey Robinson and once over allegations of misconduct regarding a passport application for the Hinduja brothers.
He was later cleared of any wrongdoing.
John Hutton, who has replaced Des Browne as defence secretary, said everyone in the Labour Party would welcome Mr Mandelson's return.
But BBC political correspondent Iain Watson said that analysis appeared to be "a little over-optimistic".
"Some backbenchers on the left have already denounced his appointment while I understand one cabinet minister tried to block it at the 11th hour," he said.
Left-wing Labour MP John McDonnell said: "This is an extraordinary step backwards into the worst elements of the Blair era, to reinstate possibly the most divisive figure in Labour's recent history."
Of course we've had our ups and downs but we have also known each other for over 20 years and originally we worked very well together
The reshuffle could force Conservative leader David Cameron to follow suit with his shadow cabinet.
The Tory party will have to take account of the changes made to the government, including the creation of a new Department for Energy and Climate Change, led by Ed Miliband.
The prime minister defended his decision to bring Mr Mandelson back into the cabinet at a news conference on Friday.
He said he needed "serious people for serious times" and it was in the "national interest" to bring in Mr Mandelson because of his experience in global trade.
Mr Brown said he wanted to "reinvent government" to cope with the new challenges of financial instability, oil price rises and food price rises.
"He has built up a reputation over the last few years as someone who can get things done," said Mr Brown.
Pressed on his long feud with Mr Mandelson, said to stem from Mr Mandelson's backing for Mr Blair as Labour leader in the 1990s, he said: "Whatever the ups and downs have been in the past, everybody has got to come together and make sure that as a nation we come through this successfully."
Other key movers in the reshuffle include Geoff Hoon, who has taken over from Ruth Kelly as transport secretary, while Nick Brown returns to the cabinet as chief whip.
Immigration minister Liam Byrne is promoted to the new role of policy co-ordinator, which is not a full cabinet role, but he will attend cabinet meetings.
Margaret Beckett replaces Caroline Flint as housing minister. Ms Flint moves to the Foreign Office as Europe minister.
Leader of the House of Lords, Baroness Ashton, replaces Mr Mandelson in Brussels.
Mr Mandelson, a former Northern Ireland and trade and industry secretary, said he was looking forward to the challenge of his new role.
Referring to his past relationship with Mr Brown, he said: "Of course we've had our ups and downs, but we have also known each other for over 20 years and originally we worked very well together and I am very proud to have been invited to serve in his government."
Gordon Brown explains why he brought Peter Mandelson back
Former home secretary David Blunkett described the appointment as a "masterstroke" and told the BBC it would unite the government.
"It is embracing someone who, in the past, had been seen as being very close to Tony Blair, so it's an inclusive measure," he said.
For the Conservatives, William Hague said it was a "stunning failure of judgement" by Mr Brown: "In bringing back Peter Mandelson - the man who created Labour spin - he has broken his promise to govern in an honest and open way."
Danny Alexander, for the Liberal Democrats, said: "Resurrecting ex-ministers from the political graveyard is not going to breathe new life into Gordon Brown's zombie government."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.