Ms Allan ran for leader of the Victorian Labor Party at a caucus meeting on Wednesday after Daniel Andrews' shock resignation less than 24 hours before.
She was sworn in late on Wednesday.
Public Transport Minister Ben Carroll will be her deputy.
"It is such a deep honour and privilege," Ms Allan told reporters.
"Twenty-four years ago, almost to the day when I walked into this place as a much younger woman from regional Victoria, I never expected to have this length of service or indeed to be able to have had the honour and privilege of serving the Victorian community in various ministerial roles.
"I pledge to continue to work incredibly hard as I have done each and every day."
The Bendigo East MP will be Victoria's second female leader and the first Labor premier from regional Victoria in almost 100 years.
She hoped her election showed women and regional Victorians they could succeed in politics.
"It says to young women, older women, women from across different backgrounds in all parts of the state that leadership takes on different shapes and sizes," she said.
Ms Allan became the youngest woman elected to Victoria's parliament in 1999 at the age of 25 and the state's youngest minister in history in 2002 at 29.
In June 2022 she stepped in as Mr Andrews' deputy and presumed successor and most recently served as minister for transport infrastructure and the suburban rail loop project.
She was also charged with delivering the now-cancelled 2026 Commonwealth Games until the portfolio was abolished.
Ms Allan paid tribute to Mr Andrews but said she had a very different style to other premiers who came before her.
Wednesday's caucus meeting was delayed after Mr Carroll threw his hat in the ring for the leadership.
But Ms Allan emerged from the meeting with the numbers to become premier, avoiding the matter going to a vote because both technically ran unopposed.
Mr Carroll said Ms Allan would make an outstanding premier and he would maintain a strong relationship with Tim Pallas, who had been picked as the left faction's contender for deputy.
"I was always keen to rise, I've had 14 portfolios across six years ... I'm always looking to see how I can continue to increase my contribution to this outstanding Labor government," Mr Carroll said.
He became the MP for Niddrie in Melbourne's northwest in 2012 and most recently served as public transport and employment minister.
The former political advisor and solicitor is a member of the party's right faction.
Opposition leader John Pesutto claimed Ms Allan avoided talking about the state's growing debt in her first press conference and seized on what he described as division between the two leaders.
"The new deputy premier doesn't believe the new premier should have the job ... that is a recipe for instability," he said.
Mr Andrews told reporters he couldn't be happier Ms Allan had taken over from him as he left parliament following the vote.
"She's always worked hard for the people of Victoria and she always will," he said.
Mr Pallas will remain treasurer and a new ministerial cabinet spot left by Mr Andrews' departure will be filled by Eltham MP Vicki Ward.
The new ministry will have to be announced and there will also be a by-election for Mr Andrews' seat of Mulgrave.
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