The star and his wife, Pamela Stephenson, have parted with Candacraig House, the baronial home in Aberdeenshire they bought in 1998.
The Big Yin used the 12-bedroom property as a Highland retreat and often hosted famous guests there, including Robin Williams, Steve Martin and Ewan McGregor.
The 17th-century house in Strathdon is set in 14 acres and includes a walled garden and a croquet lawn.
The house and surrounding estate was put up for sale last September and advertised by estate agents Savills for offers over £2.75m. The sale included four cottages in the grounds.
The sale was concluded last month. The new owner wishes to remain anonymous.
A source said: "The sale went through in the last couple of weeks and the new owner is delighted.
"It is a wrench for the Connollys to let go of the property, but they are now permanently based in New York and have been spending less and less time at Candacraig House.
"Billy and Pamela have often said he is at his happiest when he is there. It is sad for them but they are content it is going to good hands."
Interior pictures of the property showed rooms decorated in an exuberant though traditional Scottish style.
The extensive dining room, which can seat 20 peopls on red tartan chairs, has green tartan walls on which an array of stags' antlers hang.
The bedrooms also have a tartan theme and have four-poster beds with fabric curtains and traditional oak furniture.
The entrance hall has exposed stone walls, a winding staircase and chandeliers.
In 2012 the celebrity couple started renting out the property because they were spending less and less time there.
For £3950, groups of up to 11 people could hire the house for one night and have a three-course dinner cooked by the resident chef.
In the sales brochure the house was described as "a traditional Scots baronial mansion house built of harled stone under a slate roof with pepper pot turrets and steep pitched roofs."
Connolly, 71, who was diagnosed with Parkinson's disease last year, bought Candacraig House from Body Shop founder Anita Roddick for £590,000 16 years ago.
He then spent an additional £500,000 buying up the neighbouring properties to ensure greater privacy.
Although he now spends most of his time at his apartment in New York, Connolly recently said he was considering moving to the south coast of England.