Alex Lunn, who represents the Craigentinny/Duddingston ward in Edinburgh, said a Yes vote could lead to a “truly progressive” society.
“I believe the best thing for Scotland is to take this opportunity and vote Yes to independence,” he told the Edinburgh Evening News.
“To allow myself the freedom to campaign for that, I decided to join the Scottish National Party and I’m leaving my current party, the Scottish Labour Party.”
It is understood Mr Lunn recently failed in an attempt to be selected as Labour’s Holyrood election candidate for the Edinburgh Eastern ward.
Despite his defection, he will remain on the council’s administration which is a coalition of Labour and the SNP.
Andrew Burns, the Labour leader of Edinburgh City Council, said: “I’m bitterly disappointed that Alex has chosen to leave the Scottish Labour Party.
“Alex has never raised his ‘apparent’ support for independence with myself, or any group colleagues, and thus his decision to defect has come completely out of the blue.
“Obviously, this won’t affect the current coalition arrangements and we’ll continue to work as a capital coalition for the wider benefit of the people of Edinburgh.”