Ballesteros, once the top-ranked golfer in the world, died a day after his family reported his condition was quickly worsening.
His family was with him at his home in Pedrena, where he learned to play golf as a child.
The funeral will be Wednesday, Britain's Daily Telegraph reported.
"Seve was one of the most talented and exciting golfers to ever play the game," Tiger Woods said on his Web site.
The Spanish star, who broke onto the world scene with his play in the British Open as a teenager in the 1970s, inspired golfers around the world with his daring style of play, often getting out of troublesome situations with seemingly impossible shots.
Jack Nicklaus once joked Ballesteros could hit the ball "out of a garbage can" if he had to.
The flamboyant, charismatic Ballesteros, a favorite with golf fans everywhere, was diagnosed with a brain tumor in October 2008 and underwent several surgeries and rounds of chemotherapy. Last year he said he was 90 percent better -- exercising and hitting golf balls.
Ballesteros was one of the greatest players of his era.
He won his five majors -- the Masters twice and British Open three times -- between 1979 and 1988. He also starred for European teams in the Ryder Cup and won numerous events around the world, including dozens of titles on the European Tour.
Ballesteros was ranked No. 1 in the world in the late 1980s and was inducted into the World Golf Hall of Fame in 1999.
His family released a statement on his Web site saying:
"The Ballesteros family is very grateful for all the support and gestures of love that have been received since Seve was diagnosed with a brain tumor at Madrid Hospital la Paz. At this time the family asks for respect and privacy at such a painful time."
Severiano Ballesteros Sota was born April 9, 1957, in Pedrena, one of four brothers. All became professional golfers.
"I think he comes as close to a complete player as anybody I've ever seen," fellow golfer Ben Crenshaw told Sports Illustrated in 1985. "He can hit every shot in the bag and do it with the style and look of a champion."
Ballesteros is survived by two sons, a daughter and his three brothers. His marriage to Carmen Botin ended in divorce in 2008.