The Spurs and England centre-half, now 51, was rushed to hospital after suffering a circulation blockage in his left leg.
Mabbutt will remain under observation at Kings College Hospital for around two weeks, but he is expected to make a full recovery.
A statement on the Spurs website read: "The Club are delighted to report that Gary Mabbutt is now making a successful recovery from an emergency operation to cure a circulation blockage in his left leg.
"Our former captain was admitted to Kings College Hospital, London, for a peripheral artery bypass operation and will remain in hospital for a two-week recovery period.
"Everybody at the Club would like to wish him a full and speedy recovery, while Gary himself would like to thank his dedicated medical team and staff at Kings College."
Mabbutt, who began his career with Bristol Rovers, remains the longest-serving player in Spurs history having made 482 appearances in 16 years with the club before retiring in 1988.
He collected one UEFA Cup and two FA Cup winners' medals and also earned 16 caps for England.