The 70-year-old Glasgow-born star has hosted celebrities such as Sir Sean Connery, Robin Williams and Ewan McGregor at his Candacraig House in Royal Deeside.
The listing on a property website describes the property as a Scottish mansion house in a "stunning Highland setting" with four reception rooms, 12 bedrooms and 11 bathrooms.
It also details seven cottages in the grounds, a walled garden, a loch and 14 acres of woodland.
The sale of the property has sparked speculation that Connelly and his 64-year-old wife Pamela Stephenson are preparing to move to Australia.
The couple bought the house and a few acres of land for £590,000 in 1998 from Gordon and Anita Roddick, co-founders of the Body Shop chain.
Since then they have spent an estimated £1m buying back neighbouring properties and land that had originally been part of the surrounding estate.
In February last year the couple starting letting the house out to corporate clients for up to £4000 a night.