It's believed he was operated on at the Southern General Hospital in Govan two days ago.
A source close to the actor said: "It seems Tony is recovering well, although it wasn't a straightforward case of treating the prostate cancer.
"There was a tumour to deal with at the same time.
"However, he came through the operation well and is getting his strength back."
Tony, who worked as a miner before going to drama college when he was 26, is one of the country's most popular comedy actors.
His first major starring role was in Scotch and Wry but he went on to play the part of the amoral Jamesie Cotter in Rab C Nesbitt for the past 20 years. Alongside Barbara Rafferty as Ella, the ever-warring pair made up one of the most popular sitcom duos to appear on screen.
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Everyone at Scottish Actors wishes Tony a quick and full recovery.