Seve Ballesteros underwent 12 hours of surgery yesterday to remove a brain tumour and is currently "stable" in the intensive care unit of a Madrid hospital.
A biopsy had been scheduled on the tumour which was discovered last week after Ballesteros collapsed at Madrid Airport, but doctors decided to operate.
The operation passed without any complications, according to the La Paz hospital.
Ballesteros was today said in a statement from the hospital to be "conscious and in a stable condition", with a further report on his health expected to follow in the next week.
Ballesteros, 51, collapsed at Madrid Airport last week and was in intensive care for five days, with doctors releasing a statement saying that he had suffered "a partial epileptic fit".
He underwent a number of tests over the weekend which uncovered the tumour. After informing his family, Ballesteros confirmed the news in a statement on Sunday.
There have been concerns over Ballesteros' health since he retired in 2007.
Doctors discovered an irregular heartbeat when he was admitted to hospital last year, while persistent back problems led to his retirement following a brief comeback in the middle of the decade.
In a glittering career Ballesteros won the Open Championship three times, the Masters twice, and 50 European Tour events. He also captained Europe to Ryder Cup victory at Valderrama in 1997.
Today's statement from the hospital read: "At present, Severiano Ballesteros is conscious and in a stable condition, although he will not be able to receive visits in the next few days until he recovers from the surgical process."
It added: "The next medical report will be given when the patient moves to the ward, which will probably be next week."