Tayside Police said Charles Adam, who played for Dundee United and Partick Thistle, died on Monday in Dundee.
Mr Adam was the father of current Scotland international and Stoke midfielder Charlie Adam and Grant Adam, who is the goalkeeper for Airdrie United in the Scottish First Division.
A police statement said: "Tayside Police were called to Grampian Gardens in Dundee at 6.30pm on Monday after the death of a 50-year-old man.
"The deceased has been confirmed as former professional football player Charles Adam (senior) who played for Dundee United."
Police said there were no suspicious circumstances and a report will be sent to the procurator fiscal.
Stoke, who play Tottenham on Saturday, issued a short statement expressing their sympathy to their midfielder and family.
"All our thoughts are with Charlie and his family at this difficult time," said the statement.
"Out of respect to the family, players and staff at the club will not be making any press comment over the Christmas period."
Scotland Under-21 goalkeeper Grant Adam is on loan at Airdrie from St Mirren.
The Paisley club said in a statement: "It is with great sadness that we have learned that Mr Charlie Adam - father of our player Grant Adam and former St Mirren player Charlie Adam - has suddenly passed away.
"All at St Mirren Football Club would like to pass on their condolences to Grant, Charlie and their family at this sad time."
Airdrie also reacted to the news with "great sadness".
They added: "Charlie Snr had been a guest of the club earlier this year when Grant was with us originally, whilst on loan from Rangers. Our deepest condolences go out to Grant, Charlie Jnr. and the entire family."
As well as playing for Dundee United and Partick, Adam also played for St Johnstone, Brechin, Forfar and Arbroath during the 1980s and 1990s.
His former clubs paid their respects on Tuesday.
Forfar said: "He was a highly talented footballer and a larger than life character to boot.
"His son Grant followed in his Station Park footsteps with an all too short loan spell from Rangers early last season and having spoken to Charlie at Airdrie in the spring of this year when Grant played against us for the Diamonds, it came across how proud he was of his two sons' achievements in their chosen sport."
Brechin said: "Charlie was a larger than life character who played for the club from 1986-89 scoring 35 goals along the way. The club wish to extend our condolences to Charlie's family and friends."
Adam's first professional club, St Johnstone, where he scored nine goals in 28 appearances, said: "The thoughts of everyone at McDiarmid Park go to Charlie's family."
Partick, where Adam had a short spell in 1989, said: "Our thoughts and sympathies are with Charlie's family and friends at this difficult time."