A new leader will be in place in the summer, the party has said in a statement released late on Wednesday night.
It follows months of difficulties in Plaid including allegations of a sexual assault and a toxic working culture.
In his resignation letter, Mr Price said he no longer had the "united support" of his colleagues.
He said he wanted to resign in the wake of the report's findings, but was initially persuaded not to quit.
"You have my personal assurance that I will continue to serve my country, my constituents and our party with determination and enthusiasm," he said in a letter to party chairman, Marc Jones.
The announcement was made following a meeting of the party's ruling body, the National Executive Committee (NEC).
One source from the meeting said some members raised the possibility of Adam Price remaining in post.
But it was considered untenable given the seriousness of the findings of the review.
The party's Senedd group will meet on Thursday morning to agree arrangements for an interim leader.
Plaid Cymru is the third largest party in the Welsh Parliament, with 12 Members of the Senedd and three MPs in Westminster.
The pro-independence party is in a co-operation agreement with the Welsh Labour government.
Party chairman Mr Jones thanked Mr Price "for his drive and vision over the past four and a half years".
Mr Price was elected party leader in 2018, when he ousted Leanne Wood.
Welsh Conservative leader, Andrew RT Davies, said: "I have no doubt Adam Price's departure is a moment of personal sadness for him.
"Following the recent report into the culture within their party, it became clear Plaid Cymru politicians no longer had confidence in his leadership, so his departure became inevitable."
Since last year Plaid Cymru has been dogged by claims of a toxic culture in the party, and it emerged last November that an allegation of sexual assault had been made against a senior member of staff.
Separately, a serious allegation was also made about the conduct of a Member of the Senedd, Rhys ab Owen, who is now suspended from the Senedd group pending an investigation.
The party asked Nerys Evans, a lobbyist and former Plaid assembly member, to hold a review last December.
Her working group's report said Plaid needed to "detoxify a culture of harassment, bullying and misogyny".
It said too many instances of bad behaviour were tolerated, and said an anonymous survey of staff and elected members highlighted examples "of sexual harassment, bullying and discrimination".
Mr Price admitted the document left Plaid Cymru "harmed and tarnished". He apologised, but refused to quit.
In his resignation letter, Mr Price said: "On receiving the report, I informed you that I felt morally bound to step down as leader of the party in recognition of our collective failure."
"You counselled against my resignation as you felt it would make it more difficult to achieve progress in implementing the recommendations."
He said he was "persuaded by the argument that my stepping down would be an abdication of responsibility".
But he added: "It is now clear I no longer have the united support of my colleagues that would be necessary to follow this course to fruition."