The 66-year-old had a stent inserted in his neck on Boxing Day after being admitted to hospital.
He is now back home in Sunningdale, where the man who holds the record for most appearances on the European Tour is making good progress.
"It wasn’t the Christmas that the Torrances were expecting, due to Sam being hospitalised after suffering a stroke," said his long-time manager, Vicky Cuming of IMG.
"The surgery went well, though; he’s recovering nicely and looking forward to getting back on the golf course soon."
Torrance, who holed the winning putt in the 1985 Ryder Cup at The Belfry before leading Europe to victory at the same venue in 2002, had already decided to cut back on his commentary work this year.
However, he is planning to start playing a bit more again and will also still be undertaking corporate days among other events.