Mr Corbyn, who was a pupil at Adams' Grammar School in Newport, will compete with Yvette Cooper, Andy Burnham, Mary Creagh and Liz Kendall to succeed Ed Miliband.
The 66-year-old left winger has pledged to stand on a "clear anti-austerity platform".
Mr Corbyn, who has represented the Islington North seat in London since 1983, will need the support of 35 Commons colleagues to reach the final ballot.
So far only Mr Burnham, shadow health secretary, and shadow care minister Liz Kendall have received the required number of nominations.
Shadow home secretary Ms Cooper and shadow environment secretary Ms Creagh, a constituent of Mr Corbyn's, have yet to reach the target.
Announcing his candidacy, Mr Corbyn, a vocal campaigner against war and nuclear weapons, said: "This decision to stand is in response to an overwhelming call by Labour Party members who want to see a broader range of candidates and a thorough debate about the future of the party.
"I am standing to give Labour Party members a voice in this debate."