Dr Fraser, who has been sympathetic to the protest camp, said on Twitter: "It is with great regret and sadness that I have handed in my notice at St Paul's Cathedral."
The Dean of St Paul's, the Right Reverend Graeme Knowles, said he was "sorry to see him go".
St Paul's, which closed last week, could reopen to the public on Friday.
Differences over the handling of the protest are thought to have prompted his decision, says the BBC's religious affairs correspondent Robert Pigott.
The cathedral was shut over fears of "significant issues" with health and safety concerning the Occupy London Stock Exchange (OLSX) camp.
'Radical figure'
When it was first set up, Canon Fraser said he was happy for the demonstrators to stay and asked police to scale back their presence.
He has refused to sanction the use of force to remove the protesters as pressure mounts on the cathedral to join in legal action against them, considering it a resigning matter, our correspondent said.
It is understood that Canon Fraser considered his position untenable.
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http://www.bbc.co.uk/news/uk-england-15472362He fights the good fight!!!