Sonny Kiernan, 12, was found in bed at the property where he lived with his father, mother Lesley, 44, and 14-year-old sister Kaye in the west end of Glasgow on Monday evening.
His death is being treated as unexplained.
The Still Game star, 51, and his son were known for joking with each other via tweets on the social networking site Twitter, with the comic Ford affectionately calling his son "cheeky chops".
Sonny was the youngest of the actor's two children and studied at Kelvinside Academy in the city, where devastated staff and fellow pupils were struggling to come to terms with the news.
Police said a post-mortem examination is to be carried out.
The family have been given support by tributes from many of the showbiz personalities who know and work with Kiernan.
Scottish actor Greg McHugh, the creator and star of BBC Scotland series Gary: Tank Commander, said the youngster's death was "the worst news imaginable".
He tweeted: "Shocked having just learned of Ford Kiernan's loss. Thoughts to his family."
Veteran comedian Andy Cameron said: "Dreadful news about young Sonny Kiernan. My thoughts are with Ford and his family.
"Sometimes this life is impossible to understand."
Kathleen McDermott, who stars with Kiernan in the BBC Scotland sitcom Happy Hollidays, said: "My thoughts and prayers are with Ford Kiernan and his family at this very sad time."
Fife actor Jordan Young, who worked alongside Kiernan in Still Game, tweeted: "Such horrific news for Ford Kiernan and his family.
"My thoughts are with them today. Tragic."
BBC star and actor Omar Raza described the incident as a"heartbreaking start to the year", adding: "Saddened to hear of Ford Kiernan's loss. Will be praying for the whole family."
DJ Robin Galloway, who stars on Bauer stations throughout Scotland such as Clyde 2 and Forth 2, described the death as tragic and heartbreaking on Twitter, adding: "Thoughts and prayers with his family at this sad time."
Former First Minister Jack McConnell also expressed his condolences, describing Sonny's death as "devastating news".
Sonny, who was said to have a "great sense of humour", received an emotional tribute from his school which described him as a "lively, outgoing" pupil.
In a statement, officials said: "We are devastated to learn of the death of Sonny Kiernan.
"Sonny was a lively, outgoing pupil with a warm smile and a great sense of humour. He made a whole-hearted contribution to the school community, bringing infectious enthusiasm to lessons and activities.
"We shall always remember him as a cheerful boy who brightened our lives."
When Sonny was born at the Queen Mother's Maternity Hospital in 2001, Ford was asked how the couple had chosen the name.
The comedian replied: "It was a nice warm day."
The family moved after selling their five-bedroom villa in Pollokshields in November last year.
Police confirmed they were called to the property at 11.30pm on Monday.
A spokeswoman said: "Enquiries are continuing."
The tragedy comes after Ford and comedy partner Greg Hemphill reunited and announced plans for a Still Game comeback at Glasgow's Hydro arena. The run of live shows will start in the autumn.