"Today we have promised each other to be bound in love forever. We are truly blessed to share the news with you," the couple said in a statement.
The Hindu ceremony was attended by close family and a few friends.
The couple said they wanted "their wedding to be a very private affair".
The two stars were said to have married at a resort in Tuscany.
They will host a reception in Delhi for relatives on 21 December, followed by a celebration in Mumbai on 26 December to be attended by Bollywood stars and cricketers, they said.