Mr Michael also called on his closest rival for the post, Rhodri Morgan, to drop his own ambition to lead the assembly, but was swiftly rebuffed by the Cardiff West MP.
Mr Morgan repeated his determination to stand despite intense pressure from senior party figures and Downing Street to step aside.
Announcing his candidacy bid at a meeting in his Cardiff South constituency, Mr Michael said Mr Morgan and another leadership hopeful, Wayne David MEP, should join him on a "team ticket" as his deputies.
"I believe that it is in the interest of the Labour Party and the unity of Wales if Rhodri Morgan and Wayne David will work with me in order to put the Labour Party's principles into practice in the Assembly," he said. It would be a "privilege" to turn the dream of a devolved Wales into reality, he told a press conference.
Mr Morgan, who was beaten by Ron Davies for the candidacy in September, has emerged as a front-runner in the race, but is regarded by Downing Street as too much of a maverick. However, he made clear yesterday that he would not be part of a "team ticket" deal and was scathing of the suggestion that party members would not be allowed to choose their leader.
"I was not a jersey-warmer for Ron Davies and I am not a jersey-warmer for Alun Michael," he said.
"The answer is very simple. It comes in folding ballot papers. It goes right back to ancient Greece and it's called democracy and it has reached Wales, but perhaps only in patches. If this decision is not made in Wales, democracy and devolution don't count for anything."
Don Touhig, secretary of the Welsh Labour MPs and chairman of the party's task force charged with finding a method to replace Mr Davies, said he favoured the "team ticket" idea.
"The resignation of Ron Davies has created a situation no one wanted or could have expected. We believe the best way forward would be to have a unity ticket involving all three people, behind which the whole of the Labour Party in Wales could unite," he said.
The Wales Labour Party executive cleared the way for Mr Michael's candidacy on Monday when it reopened its list of candidates for the assembly.
Peter Hain, a Welsh Office minister and Mr Michael's campaign manager, called for the party to unite around a "team of all the talents".
"The leadership of the National Assembly is a big job at a big moment in Welsh history and you need a big figure to lead it," he said.
Nigel Evans, the Tories' spokesman for Welsh Affairs, accused Downing Street of a "control freak tendency" and said it was prepared to do anything to stop Mr Morgan becoming leader.
"The press ganging of Alun Michael for the leader's job in Wales shows how wafer-thin government confidence in devolution really is," he said.