Yates was born in Lawrenceburg, Indiana, the son of Robert and Alice Ware Yates. He attended Lockland Wayne High School in nearby Cincinnati, leading the team the Ohio high school basketball championship title in 1952, a team on which his brother, Fletcher, also starred. He graduated in 1954. Because he was offered only partial scholarships to the University of Cincinnati and Xavier University, he worked for a year while playing on a barnstorming basketball team before joining the U.S. Air Force. He was stationed at Ellsworth Air Force Base, got married in 1958, and also continued to play basketball in the military, in which he served until 1959.
He decided to pursue college basketball again, even though he was now 22. This time he accepted a partial scholarship offer from Cincinnati, and he played on the freshman team in 1959–60. In his sophomore season of 1960–61, the now 23-year-old "Gramps", as he was nicknamed by players, was a starting guard for the Bearcats.
As a point guard, Yates was known for his outstanding floor leadership and defensive ability. In 1960–61, Yates averaged 7.4 points and 2.7 assists per game as the Bearcats went 27-3, won the Missouri Valley Conference (MVC), and advanced to the NCAA championship game. Cincinnati defeated Ohio State 70-65 to claim the national crown.
As a junior in 1961–62, Yates averaged 8.2 points per game and led the Bearcats in assists with 4.3 per game. The Bearcats posted a 29-2 record, again won the MVC and again advanced to the 1962 national championship game. Cincinnati again faced Ohio State, and again the Bearcats bested the Buckeyes, 71-59, to capture their second consecutive national title. Yates earned second-team All-American honors from the Helms Foundation and was named honorable mention All-American by United Press International (UPI).
As a senior in 1962–63, Yates averaged 7.6 points and 4.1 assists per game. The Bearcats won the MVC title once again and posted a 26-2 record, advancing to the national title game for the third consecutive year. However, they fell in the finals 60-58 in overtime to Loyola University Chicago. Yates was again named All-MVC as well as first team All-American by the Helms Foundation, third-team All-American by the Associated Press (AP) and honorable mention All American by UPI and The Sporting News.
In tribute to Yates' defensive prowess, he was a three-year winner of the Bearcats' Best Defensive Player award for his efforts in helping UC finish fourth and first, respectively in the 1962 and 1963 NCAA national defensive rankings.
Yates was drafted by in the fifth round (41st overall) of the 1963 NBA draft by the St. Louis Hawks.
He returned to the University of Cincinnati as an assistant coach under Tay Baker and Gale Catlett from 1972 to 1974. In 1974–75, Yates became an assistant coach at the University of Illinois on the staff of coach Gene Bartow, and the following season under new coach Lou Henson. The team posted mediocre records Henson's first three seasons, but the Illini won 19 or more games the next five seasons with Yates serving as top assistant, and the team made two NCAA tournament appearances and two NIT appearances.
Known as a top recruiter, Yates served as an Illinois assistant for nine seasons, through the 1982–83 season.
For the 1983–84 season, Yates was named head coach at his alma mater, the University of Cincinnati, for a squad which had gone 11-17 the previous season under coach Ed Badger. Inheriting a depleted team with few scholarship players, the Bearcats posted a 3-25 record in Yates' first season of 1983–84. However, in 1984–85, with an infusinon of talent including guard Roger McClendon and forward Myron Hughes, Yates' team rapidly turned around their fortunes and posted a 17-14 record, earning an NIT berth.
In 1985–86, the team struggled again, going 12-16, followed by seasons of 12-16, 12-16, and 11-17. In 1988–89, Yates' sixth as head coach, the team returned to its winning ways, posting a 15-12 record. However, it wasn't enough as Yates was fired and later replaced by Bob Huggins. Yates' UC career ended with a record of 70-100.
Tony Yates and his wife, Maxine, are the parents of children Anthony and Brianna.
After coaching at Cincinnati, Yates, who had been a passive investor in a Cincinnati area automobile dealership owned by Longtime UC booseter Jeff Wyler, took an active management role with the firm.
Yates and golf pro Zachary Fink founded the Caring for Kids Foundation, a Cincinnati non-profit to "uplift, assist, and train youth and their families."
In 1985, Yates was inducted into the University of Cincinnati Athletics Hall of Fame.