Wilkinson's mother died when he was seven, and his father sent him to the Shattuck School in Faribault, Minnesota, where he excelled in five sports and graduated in 1933. He enrolled at the University of Minnesota, where, as a guard and quarterback for head coach Bernie Bierman, Wilkinson helped lead the Golden Gophers to three consecutive national championships from 1934 to 1936. He also played ice hockey for the University of Minnesota. Following his graduation in 1937 with a degree in English, he led the College All-Stars to a 6–0 victory over the defending NFL champion Green Bay Packers in Chicago on August 31.
Wilkinson briefly worked for his father's mortgage company, then he became an assistant coach at Syracuse University and later at his alma mater, Minnesota. In 1943, he joined the U.S. Navy, where he was an assistant to Don Faurot with the Iowa Pre-Flight Seahawks football team. He served as a hangar deck officer on the USS Enterprise. Following World War II, Jim Tatum, the new head coach at the University of Oklahoma, persuaded Wilkinson to join his staff in 1946. After one season in Norman, Tatum left the Sooners for the University of Maryland. The 31-year-old Wilkinson was named head football coach and athletic director of the Sooners.
In his first season as head coach in 1947, Wilkinson led Oklahoma to a 7–2–1 record and a share of the conference championship, the first of 13 consecutive Big Six/Seven/Eight Conference titles. Ultimately, Wilkinson became one of the most celebrated college coaches of all time. His teams captured national championships in 1950, 1955, and 1956, and they amassed a 145–29–4 (.826) overall record.
The centerpiece of his time in Norman was a 47-game winning streak from 1953 to 1957, an NCAA Division I record that still stands. It has been moderately threatened only three times: by the Toledo (35 wins, 1969–1971), Miami (FL) (34 wins, 2000–2003), and USC (34 wins, 2003–2005). Earlier, the Sooners ran off 31 consecutive wins from 1948 to 1950. Apart from two losses in 1951, Wilkinson's Sooners did not lose more than one game per season for 11 years between 1948 and 1958, going 107–8–2 over that period. His teams also went 12 consecutive seasons (1947–1958) without a loss in conference play, a streak which has never been seriously threatened. Wilkinson did not suffer his first conference loss until 1959 against Nebraska, his 79th conference game.
While coaching at OU, Wilkinson began writing a weekly newsletter to alumni during the season, to keep them interested in Sooner football. He also became the first football coach to host his own television show. He and Michigan State University coach Duffy Daugherty partnered to sponsor a series of clinics for high school coaches nationwide. Later, they turned their clinics into a profitable business.
Following the 1963 season, his 17th at Oklahoma, Wilkinson retired from coaching at the age of 47. Along with Bennie Owen, Barry Switzer and Bob Stoops, he is one of four football coaches to win over 100 games at the University of Oklahoma. No other college football program has had more than three coaches who accomplished the feat.
While at Oklahoma, Wilkinson served on the President's Council on Physical Fitness from 1961 to 1964. He designed 11 floor exercises for schoolchildren that were incorporated into the song "Chicken Fat", the theme song for President John F. Kennedy's youth fitness program, which was widely used in school gymnasiums across the country in the 1960s and 1970s.
In February, 1964, Wilkinson announced that he would enter a special election to replace his friend, the late Robert S. Kerr, as U. S. Senator from Oklahoma. He had already resigned his position as head coach of the Oklahoma University Sooners. Politicians and the Oklahoma press debated whether he was qualified to become a U. S. Senator, though all seemed to agree that his popularity as a cultural icon gave him an important edge. Easily winning the Republican primary, Wilkinson became the Republican nominee for the U.S. Senate in 1964, at which point he legally changed his first name to Bud, but narrowly lost to Democrat Fred R. Harris, then a State Senator in Oklahoma. Both parties involved political heavyweights from out of state to campaign for their candidates. Republicans invited former President Eisenhower and Senator Barry Goldwater. Wilkinson's Republican advisers brought in Senator Strom Thurmond to appeal to ultra-conservative voters in Little Dixie, which had recently turned reliably Republican. That effort backfired. In the 1964 General Election, Republican presidential nominee, Senator Barry Goldwater lost to incumbent President Lyndon Baines Johnson 55-45 percent in Oklahoma. Through 2016, Johnson is the last Democrat to carry Oklahoma in a presidential election. Wilkinson served as Republican National Committeeman from Oklahoma, and was considered for the position of committeeman chairman by Richard Nixon but was not selected. Wilkinson entertained seeking the other Oklahoma U.S. Senate seat in 1968, but he did not run, and the position went to former Governor Henry Bellmon, also a Republican.
In 1965, Wilkinson joined ABC Sports as their lead color commentator on college football telecasts, teaming with Chris Schenkel and, later, Keith Jackson. Wilkinson was the color analyst for three of the greatest games in college football history, each commonly referred to as a "Game of the Century": Notre Dame vs. Michigan State in 1966, Texas vs. Arkansas in 1969, and Nebraska vs. Oklahoma in 1971.
Wilkinson was inducted into the College Football Hall of Fame in 1969. In 1978, Wilkinson returned to coaching with the St. Louis Cardinals of the NFL. After less than two disappointing seasons, he was fired, and returned to broadcasting with ESPN.
Wilkinson suffered a series of minor strokes and, on February 9, 1994, he died of congestive heart failure in St. Louis at the age of 77. He is interred at Oak Grove Cemetery in St. Louis, Missouri.
Wilkinson was married to the former Mary Schifflet in 1938, with whom he had two sons, Pat and Jay. They divorced in 1975. A year later, he married Donna O'Donnahue, 33 years his junior, who survived him in death.