Royal died Wednesday in Austin, a release on the Texas football website stated. He was afflicted with Alzheimer's disease.
Royal was inducted into the College Football Hall of Fame in 1983 after a 23-year career in which his teams were 184-60-5. He never had a losing season.
He coached at Texas for 20 seasons and had undefeated teams in 1963 and 1969. Texas was voted national champions after the '63, '69 and '70 seasons.
The Longhorns were 167-47-5 under Royal and won 11 Southwest Conference titles and played in 16 bowl games.
"Today is a very sad day. I lost a wonderful friend, a mentor, a confidant and my hero. College football lost maybe its best ever and the world lost a great man," said Texas Coach Mack Brown, whose 133 wins at Texas is second all-time behind Royal at the school.
"I can hardly put in words how much Coach Royal means to me and all that he has done for me and my family. I wouldn't even be at Texas without Coach."
Royal was born July 6, 1924 in Hollis, Okla. He was recruited to play at the University of Oklahoma by scouts who saw him playing for a U.S. Army Air Corps team during World War II.
He played quarterback and defensive back at Oklahoma and turned to coaching after his playing days. He coached at Mississippi State for two seasons and Washington for one before taking over at Texas in December 1956.