Dr Fraser made the announcement on his Twitter page this morning. He said the decision had been made with "great regret and sadness".
In a statement to the Guardian, he elaborated that he feared the cathedral chapter has "set on a course of action that could mean there will be violence in the name of the church".
The Dean of St Paul's, the Rt Rev Graeme Knowles, said today that he was "very sorry" to see the chancellor go.
"Giles has brought a unique contribution to the life and ministry of St Paul's and we will be very sorry to see him go," he said in a statement.
"He has developed the work of the St Paul's Institute and has raised the profile of our work in the City.
"We are obviously disappointed that he is not able to continue to his work with Chapter during these challenging days. We will miss his humour and humanity and wish Giles and his family every good wish into the future."
In a separate statement last night, the Dean said St Paul's planned to reopen on Friday following "significant changes to the layout of those dwelling in tents outside".
"The staff team here have been working flat out with the police, fire brigade and health and safety officers to try to ensure that we have confidence in the safety of our worshippers, visitors and staff which will allow us to reopen," he said.
"We have been and continue to take legal advice on a range of options including court action. Chapter very much hopes that we will achieve a peaceful solution."
The cathedral took the controversial decision to close last week after dozens of tents sprang up around the building as part of the Occupy London Stock Exchange demonstration.
Dr Fraser has been vocal in his support of the protesters, telling them they were welcome when they first started arriving outside the cathedral nearly two weeks ago.
His resignation was greeted with sadness by the Bishop of Whitby, the Rt Martin Warner.
He tweeted: "Sorry about Giles Fraser's resignation. Good Chapter government should benefit from the strengths of its members, not expose the weaknesses."
The cathedral's handling of the protest outside its doorstep has divided Anglicans. The Bishop of London, Dr Richard Chartres, said earlier in the week that the protesters should leave.
The Rev George Pitcher, from St Brides Church in Fleet Street and a friend of Dr Fraser, told Premier Christian Radio that the Church of England "risks damaging its reputation for a generation".