The Sydney MP said he is honoured to be taking on the top job.
"Thank you to members of caucus, rank and file members and affiliates for your support," he posted on Facebook.
"Together we can return our great party to government in three years time."
Mr Albanese has promised to talk to voters outside the Canberra and Labor bubbles in a bid to convince them his party can better represent them.
Mr Albanese will hold a press conference at midday.
Victorian MP Richard Marles is in line to be his deputy, again being the only person with his hat in the ring for the job on Monday.
Both men have promised to talk to voters who didn't vote Labor in a bid to make sure they understand last Saturday's shock election loss.
"It's really important that we understand what happened at the election. It's important we make sure we're talking to the widest range of people we can," Mr Marles said on Sunday.
Mr Albanese has also promised to talk to voters outside the Canberra and Labor bubbles in a bid to convince them his party can better represent them.
Labor has had a man and woman in the leadership team since 2001, except for a three-month stint in 2013 after Kevin Rudd got his revenge on Australia's first female prime minister Julia Gillard.
But Victorian MP Clare O'Neil dropped out of the race for deputy after her colleagues told her she needed more experience bringing the party together behind a leader.
"Richard Marles has got the skills and the qualities and the experience at this stage to be able to do that job really well," she said.
Mr Marles said it was important to maintain the party unity that Bill Shorten instilled in Labor after the tumultuous Rudd-Gillard years.
"Certainly I hope I can be a force for unity in the party," he said.
Labor's entire front bench also faces a shake-up following last weekend's unexpected federal election loss.
