Born in Westerly, Rhode Island, Gavitt graduated from Dartmouth College in 1959, where he was a member of the 1959-1960 varsity basketball team, the last Dartmouth basketball team to win the Ivy League championship. He spent two years as an assistant basketball coach at Worcester Academy before becoming an assistant coach at Providence under the legendary Joe Mullaney in 1962. He left in 1966 to become assistant coach and then head coach at his alma mater before taking over for Mullaney at Providence in 1969.
Under his ten-year tenure, the Friars advanced to the postseason eight straight years (1971–78; five NCAA appearances, 1972-'74, '77-'78, and three NIT appearances, 1971, '75, 76). In 1973, Gavitt's team made it to the Final Four for the first time in school history. He also served as director of athletics at PC from 1971 to 1982, and was at that position when the school's women's athletics programs were started as a result of Title IX.
In 1979, Gavitt, along with several other college athletics administrators, helped to form the Big East Conference as a means to better compete with the major schools in the country. He became the conference's first commissioner, from 1979 to 1990. Under his direction, the Big East steadily expanded and was an almost immediate success, as several schools became basketball powerhouses (culminating in the 1985 Final Four, in which three schools from the conference - Georgetown, Saint John's, and eventual champion Villanova - were present).
During his tenure, six of the conference's schools (Georgetown, Villanova, Saint John's, Providence, Seton Hall and Syracuse) participated in the Final Four, and all nine teams made it to the NCAA tournament at least once. His contributions are memorialized in the Dave Gavitt Trophy, given to the winner of the Big East's men's basketball tournament, which he was responsible for not only creating, but its annual use of Madison Square Garden. Also, from 1982 to 1984, he was chairman of the NCAA Division I Basketball Committee. It was under his guidance that the tournament expanded to sixty-four teams, in order to provide better opportunity for small conference teams to participate. He was also responsible for the playing of Final Four games in larger venues such as domed stadiums, and the first full contract with a television network to provide universal coverage of the tournament, further adding to the tournament's popularity and prestige.
Gavitt has also been involved in Olympic basketball. In 1980, he was selected as the head coach of the Olympic basketball team, only to lose out on the opportunity due to the boycott of the Moscow games by the United States. He would also go on to serve on the Olympic governing body, including a presidency from 1988 to 1992. It was during his tenure that he developed the concept of the "Dream Team," an Olympic basketball team composed of the NBA's best.
Besides these responsibilities, Gavitt was CEO of the Boston Celtics from 1990 to 1994, President of the NCAA Foundation from 1995 to 1997, and Chairman of the Board of the Naismith Memorial Basketball Hall of Fame until 2003. He is a member of the Providence College Athletic Hall of Fame (1984), National Association of Collegiate Directors of Athletics Hall of Fame (2000), and the International Scholar-Athlete Hall of Fame (2000). Gavitt was inducted into the Basketball Hall of Fame on September 8, 2006. He became the third former member of the Friar athletic program (after John Thompson and Lenny Wilkens), and the first native of Rhode Island to be enshrined. The court at the Dunkin' Donuts Center, Friar's home court, in Providence, Rhode Island is named after him.
National champion Postseason invitational champion Conference regular season champion Conference regular season and conference tournament champion Division regular season champion Division regular season and conference tournament champion Conference tournament champion