Reaves was born in Anniston, Alabama in 1950, but moved to Tampa, Florida with his mother and grandmother after his father died when he was 9 years old. He attended T.R. Robinson High School in Tampa, where he was a star high school football quarterback for the Robinson Knights. As a senior in 1967, he led the Knights to the Florida Class 2A football semifinal game before losing to the Coral Gables Cavaliers, who won the state championship and were ranked as the national champions afterward. Reaves was lauded as the State Player of the Year. He also played basketball and baseball and ran track for the Knights, and once scored fifty-two points in a high school basketball game.
In 2007, thirty-nine years after he graduated from high school, the Florida High School Athletic Association (FHSAA) recognized Reaves as one of the "100 Greatest Players of the First 100 Years" of Florida high school football.
After graduating from high school, Reaves accepted an athletic scholarship to attend the University of Florida in Gainesville, Florida, and played quarterback for coach Ray Graves and coach Doug Dickey's Florida Gators football teams from 1969 to 1971. In his first season as the Gators' starting quarterback, Reaves was part of a group of second-year star players known as the "Super Sophs" that included Reaves, wide receiver Carlos Alvarez and running back Tommy Durrance. Reaves and the Super Sophs led the Gators to their all-time best season record of 9–1–1, and an upset 14–13 victory over the Tennessee Volunteers in the 1969 Gator Bowl. Reaves and Alvarez subsequently broke every Florida passing and receiving record during their three-season college careers, and Reaves set the National Collegiate Athletic Association (NCAA) career passing record of 7,581 yards and the Southeastern Conference (SEC) career record of fifty-six touchdowns. Reaves was a first-team All-SEC selection in 1969, a first-team All-American in 1971, and a team captain in 1971. As a senior, he received the Sammy Baugh Trophy, recognizing the nation's best college passer, and the Gators' Fergie Ferguson Award, recognizing the "senior football player who displays outstanding leadership, character and courage."
His record as the NCAA's all-time career leader in passing yards was achieved after a controversial fourth-quarter play in the last game of the 1971 regular season, when most members of the Florida Gators defense laid down on the field in the fourth quarter, allowing the Miami Hurricanes to score a touchdown with enough time for Florida's offense to get the ball back so Reaves could set the record. The event is commonly referred to as the "Florida Flop," and is often recalled bitterly by Hurricanes alumni and fans.
Reaves returned to Gainesville during the NFL off-season and completed his bachelor's degree in business administration in 1973, and he was later inducted into the University of Florida Athletic Hall of Fame as a "Gator Great" in 1985. He was picked as No. 30 among the 100 greatest Gators from the first century of the Florida football program by The Gainesville Sun in 2006.
Reaves jumped to the expansion Tampa Bay Bandits of the start-up USFL in 1983; he was the Bandits' starting quarterback for three seasons under head coach Steve Spurrier in a pass-oriented offense. He only played eight games of the 1983 season because of a wrist injury. However, he still managed to complete 139 passes out of 259 attempts. He threw for 1,276 yard, but tossed 16 interceptions compared to nine touchdown passes. He bounced back in 1984, going 313 out of 544, tossing for 4,092 yards, and tossing 28 touchdowns, compared to 16 interceptions. This was the only USFL season in which he threw more touchdowns than interceptions. In the league's final season, 1985, he was 314 for 561, tossed 29 interceptions compared to 25 touchdown passes.
After the USFL dissolved after the 1985 season, Reaves returned to the NFL for one final season with the Tampa Bay Buccaneers in 1987. Reaves' NFL career was that of a journeyman back-up—and his NFL career total of 3,417 yards showed it. In Reaves' two seasons as the Bandits' full-time starting quarterback, however, he threw for over 4,000 yards passing both years (1984 and 1985), and just over 10,000 total yards in his three-season USFL career (1983–85).
Reaves was an assistant football coach for the Florida Gators under head coach Steve Spurrier from 1990 to 1992 and again in 1994, working primarily with the Gators quarterbacks, including Shane Matthews. He left Gainesville to become an assistant coach for the South Carolina Gamecocks under head coach Brad Scott from 1995 to 1997.
Reaves was arrested on gun and drug possession charges in 2008. Reaves entered an Atlanta area substance abuse rehabilitation program in May 2009.