The battle will be between four young former Cabinet colleagues and one outsider – Jon Cruddas, a Left-wing backbencher.
Mr Miliband’s younger brother Ed, 40, is expected to announce his candidacy at the weekend, leading to an inter-family battle for Labour’s top job.
Ed Balls, 43, a close ally of Gordon Brown, is almost certain to run.
The Daily Telegraph understands that Andy Burnham, 40, the former health secretary, also plans to stand but will not announce his candidacy immediately.
Mr Miliband, 44, flanked by supporters in front of the main entrance to the Commons, called for a “comradely” contest.
After paying tribute to Mr Brown, he said: “I will stand as a candidate. I do so with humility in face of the responsibility this post brings and passion for the causes and values that led me to join our party.”
He will formally launch his campaign in his constituency of South Shields next week, and said he would spend the next week visiting constituencies that Labour had lost, “listening” to voters’ concerns. Mr Miliband said the country had entered a “new era” and Labour needed a period of “deep renewal”.
He said the Liberal Democrat-Conservative coalition government put new responsibility on Labour to represent those with centre and Left of centre opinions.
Most of Mr Miliband’s rivals will delay their announcements until next week, and the former foreign secretary’s decision to announce his candidacy raised eyebrows in Westminster.
He is thought to have been keen to be clear about his ambitions, having been accused of ducking several opportunities to challenge Mr Brown in the past.
Mr Miliband is the bookies’ favourite to succeed Mr Brown at 1-3.
He received a boost when Alan Johnson, the popular former home secretary, said he would not stand.
Mr Johnson and Caroline Flint, the former Europe minister, both said they would back him.
Explaining his decision, Mr Johnson, who will turn 60 next week, said: “It’s probably best if the baby boomers do something else, particularly as we have such an exceptional pool of talent there.”
The contest is likely to take weeks or even months, with the timetable expected to be announced by Labour’s ruling National Executive Committee next week.
At a meeting of the Parliamentary Labour Party, Harriet Harman, the acting leader, called for an open contest in which candidates behaved “generously” to each other.
While Mr Brown said he wanted a result by the party’s conference in September, Mr Miliband’s supporters would prefer a quick contest to capitalise on his early popularity.
Ed Miliband, the former energy secretary, was expected to stand aside for his brother, but changed his mind after being urged to run.
Mr Cruddas is said to be taking soundings after receiving “many calls and emails”.
Mr Burnham also plans to bide his time.
• An account of the leadership pact made between Tony Blair and Mr Brown will be published next month when Alastair Campbell, the former Prime Minister’s spokesman, expands the first volume of his political diaries.