"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.
Many celebrities sent their best wishes to the couple.
After the celebrations in India, the couple will travel to South Africa where Mr Kohli will prepare for India's forthcoming tour there which is taking place early next year.
In the new year, Ms Sharma will return to Mumbai, where the couple will live, to resume her acting commitments.
Photo copyright: AFP. Caption: The two Indian stars wed at a resort in Tuscany