The former foreign secretary is the first contender to declare their interest in succeeding Gordon Brown, who quit as leader and PM on Tuesday. Earlier Home Secretary Alan Johnson ruled himself out of the contest and gave his backing to Mr Miliband.
The party hopes to have a new leader in place by the end of July.
Deputy leader Harriet Harman has taken over as acting leader in the meantime.
Announcing his candidacy outside the House of Commons, Mr Miliband paid tribute to Gordon Brown as a "towering figure" and wished the new Conservative-Liberal Democrat government well.
He said he was standing because he believed he could help Labour "rebuild" itself as a force for "social and economic change" in the country while in opposition.
"We have achieved a great deal in government but this is a new era with new dangers, opportunities and possibilities," he told journalists.
He described the Conservative-Lib Dem alliance as a "momentous moment in British politics".
"It puts an enormous responsibility on the Labour Party to be a great unifying force for all shades of centre and centre-left opinion in this country," he added.
Mr Miliband said he hoped the contest would attract a wide range of candidates.
In addition to David Miliband, others likely to put themselves forward include former schools secretary Ed Balls and Labour MP Jon Cruddas. Former ministers Ed Miliband - David's brother - and Andy Burnham could also enter the frame.
Former Work and Pensions Secretary Yvette Cooper has also ruled herself out from the race while another former minister, Caroline Flint, has backed David Miliband.
Mr Johnson, who ran for the deputy leadership in 2007 but lost to Harriet Harman, said the party was in "good nick" but needed to "refresh itself" after 13 years in power.
Stressing that Labour had an "exceptional pool of talent" in its ranks, the 59-year old said he felt Labour needed a younger leader to take the party forward and endorsed David Miliband.
"I think David is the greatest talent. I think he's a remarkable politician. And I think his talent is to put very complex ideas into clear language."
The BBC's Political Correspondent Reeta Chakrabarti said there was a strong body of support within the party for David Miliband but that his brother also had many admirers.
Mr Johnson also said Labour had an "important role" to play in opposition against the new Conservative-Lib Dem coalition government
"We are the only opposition," he said. "I don't think this will be a socially progressive alliance. It is our job to prove that."
Ms Cooper said it was not the "right time" for her to consider a leadership bid but she wanted to remain "part of a strong Labour team". She urged a period of "short reflection" before candidates declared their intentions.
Former Welsh Secretary Peter Hain - who confirmed he would not be standing - said the party needed "some new thinking" on the issues of political reform, social justice, equality and the environment.
"We can't keep on running the old New Labour record," he said.
Former Cabinet minister Hazel Blears said the new leader needed to understand "bread and butter issues".
"We want to see new ideas, moving beyond the 'Blair and Brown' old politics," she told the Daily Politics.
The new leader is elected by an electoral college where the votes of MPs and MEPs count for a third of the total, the votes of Labour Party members count for a third and votes of trade unions and other affiliate organisations' members count for a third.