Rudd, who was prime minister before being replaced by Gillard in 2010, resigned as foreign minister Wednesday while on a visit to the United States.
Rudd said he would seek the leadership of the Labor Party and to be the prime minister during a vote set for Monday.
Speaking to reporters in Brisbane, Rudd said he was "sick and tired" of being blamed for the failures of his successor's government, The New York Times reported.
Before his resignation as foreign minister, there had been rumors he might be sacked.
"Rightly or wrongly, Julia [Gillard] has lost the trust of the Australian people. And starting on Monday I want to start restoring that trust," CNN quoted him as saying Friday in Brisbane. "And that is why I've decided to contest the leadership of the Labor Party."
In the wake of Rudd's resignation, Gillard had called for a vote Monday to end speculation about the leadership.
Gillard's approval ratings have dipped, but CNN quoted her as saying she has enough support to lead the party to victory in the next election.
"As prime minister I have got big reforms done that languished under my predecessor," she said.
Rudd said it was clear the party had much work to do to regain public confidence and that he is best suited to do it.
"I want to finish the job that the Australian people elected me to do when I was elected by them to become prime minister," Rudd said.