During his senior year, he was co-captain of the football, basketball and baseball teams. In basketball, he averaged 15 points a game. In baseball, he hit .384 and played center field when he wasn't pitching.

In the rush-first option offense run by Greenwich High School, he completed only 41 percent of his throws for 1,220 yards, but he ran the ball 267 times for 1,928 yards and 13 touchdowns.

Young played college football for Brigham Young University, setting school and NCAA records en route to being runner-up for the 1983 Heisman Trophy. Young is a great-great-great-grandson of Brigham Young, second president of The Church of Jesus Christ of Latter-day Saints for whom BYU is named.

Young was selected by the Los Angeles Express in the first round (11th overall) and signed a record ten-year, $40 million contract in March 1984. He agreed to take his salary in the form of an annuity paid out over forty years to help the fledgling team, but the league ceased operations two years later, and Young received only a $1.4 million settlement on the annuity.

Soon after the Express decided to suspend operations for the 1986 season, Young bought out his Express contract and signed with the Tampa Bay Buccaneers, who had made him the first pick in a supplemental draft of USFL and CFL players a year earlier. During his two seasons with Tampa Bay, Young went 3-16 as a starter. Considering him a bust, the team drafted QB Vinny Testaverde first overall in the 1987 NFL Draft.

Young was traded to the San Francisco 49ers on April 24, 1987 to serve as a backup to Joe Montana. 49ers coach Bill Walsh was impressed by Young's natural abilities, and believed his lackluster numbers were primarily due to the lack of talent around him in Tampa Bay.

The San Francisco 49ers had his No. 8 jersey retired during a halftime ceremony against the New England Patriots on October 5, 2008.

Originally developed by Walsh during the 1960s while he was an assistant with the Cincinnati Bengals, the West Coast Offense is based on the idea of throwing a lot of quick, timed, high-percentage passes in order to keep control of the ball. While other teams had used ball-control offenses before, they were usually built around the running game. Walsh's strategy was unique in that it maintained the ball-control aspect, yet allowed for big plays as well since it was designed for wide receivers to pick up large chunks of yards after the catch.

Young played behind Montana for four years, but shone as a backup, throwing 23 touchdown passes and only six interceptions.

His 1988 scramble against the Minnesota Vikings was featured in a 2006 Burger King commercial with the Burger King "King" digitally superimposed over Young who eventually stumbles and falls into the end zone.