Ms Allan fell on her sword on Tuesday morning ahead of a caucus meeting where she was expected to lose a spill motion.
Ms Allan, from the party's left faction, had refused to step down on Monday after a cross-factional delegation, including six ministers, informed the embattled leader she had lost majority support of the caucus.
She had flagged her intention to nominate for the leadership if it went to an internal vote, as did Mr Carroll after being approached by colleagues.
"After speaking with my colleagues overnight, I have made the difficult decision to step aside as leader of the Victorian state parliamentary Labor Party, and as premier of Victoria," Ms Allan said.
Her resignation paves the way for Mr Carroll, her deputy and the state education minister, to be appointed her successor uncontested.
Unless another candidate nominates, it would avoid a weeks-long election process involving votes of Labor MPs and rank-and-file members, four months out from the Victorian state election.
"I will shortly chair a caucus meeting to elect a new leader," Ms Allan said.
"Should Ben Carroll emerge as our next Labor leader and Labor premier, he will have my congratulations and unqualified support."
Mr Carroll, from the party's smaller right faction, was swarmed by media as he exited a car and entered parliament through a side door.
"Right now my focus is on talking to my colleagues and I will have more to say later," he said on Tuesday.
Attorney-General Sonya Kilkenny, Economic Growth and Jobs Minister Steve Dimopoulos and outgoing Labor MP Mary-Anne Thomas earlier professed their support for the premier.
Federal Foreign Minister Penny Wong said politics was a tough game and good people had to do "difficult things" at times.
"I will leave it to them to resolve," she told ABC TV.
"Obviously, whatever the outcome, we will be working with them in the lead-up to state election."
Parliament is also set to debate an opposition no-confidence motion in the premier and government, which can trigger an early election in the unlikely event it passes.
"This is a unique opportunity for Labor members of parliament not to stab their boss in the back in a side room in parliament," Shadow Attorney-General James Newbury said.
There was no guarantee Mr Carroll can lead Labor to a record fourth-straight election victory if he were to become premier, Redbridge pollster and former Liberal strategist Tony Barry said.
A significant cabinet reshuffle and policy overhaul would be needed to differentiate Mr Carroll's politics from Ms Allan's and subsequently remedy the drop in voter support for Labor incurred under her leadership, Mr Barry said.
"There's going to have be changes around the Suburban Rail Loop and other things where he differentiates himself from Jacinta Allan," he said.
"Otherwise he's going to be completely open to the attack of same horse, different jockey.
"In that situation, he might make a bad situation even worse."
Ms Allan has faced mounting pressure in recent months following revelations of corruption on Big Build projects.
She has refused to call a royal commission into the sector after corruption-busting lawyer Geoffrey Watson estimated it had cost the state $15 billion.
Persistent crime and a failure to reach a pay deal with public school teachers have also dogged the government.
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