The party's 2015 election manifesto promised to abolish the elected roles, created by the coalition government.
But Mr Corbyn described their role as "vital in a changing world".
He was speaking as he launched Labour's campaign for the police and crime commissioner elections to be held across England and Wales on 5 May.
The commissioners, who replaced the previous model of police authorities, have powers to hire and fire chief constables and set police strategy and budgets.
They were first elected in November 2012 on a historically low turnout.
Speaking in Birmingham, Mr Corbyn said his party had been "not necessarily in favour" of the establishment of police and crime commissioners but added: "We are going to keep them, we're going to make them more accountable, make it more democratic."
He said accountability was a "fundamental principle" of public services like the police.
On his party's campaign, he added: "We want to return to the principle we introduced as a Labour government on community policing - policing by consent, and that's exactly what our candidates for police and crime commissioners are determined to do."
He also criticised cuts to police budgets, adding: "It is disgraceful that when the police are more vital than ever to keeping people safe, their numbers are being reduced."
The government has rejected Labour's attack on police budgets. Speaking in a Commons debate on Wednesday, Home Secretary Theresa May said overall police spending would increase to Â£12.3bn by 2020.
Forces also have the power to raise extra money through council tax.
Labour plans to retain the posts of police and crime commissioners and make them "more accountable", Jeremy Corbyn has said.