He played college football for the Baylor Bears, where he won the Jim Thorpe Award.
As a freshman, he began the year at running back and was named the starter at cornerback halfway through the season.
As a sophomore, he began the season at corner, but was moved to free safety in the second game, where he blossomed and collected 99 tackles.
As a senior in 1986, Everett became the first-ever winner of the Jim Thorpe Award as the nation's top defensive back.
[3] Everett was selected by the Pittsburgh Steelers in the fourth round (94th overall) of the 1987 NFL draft,[4] after dropping because he was considered too small to play safety.
As a rookie, he quickly established himself as a punishing hitter and was named the starter at free safety in the eighth game of the season against the Miami Dolphins.
On September 19, 1992, after having missed the first two games due to a contract dispute, he was traded to the Cowboys in exchange for a fifth round draft choice (#140-Marc Woodard).
The Cowboys went on to win Super Bowl XXVII, with Everett recording 6 tackles, two interceptions, one fumble recovery and one sack in the 52–17 victory over the Buffalo Bills.
On April 2, 1994, because of salary cap reasons he was traded to the Tampa Bay Buccaneers in exchange for a fourth round draft choice (#109-Willie Jackson).
Everett was one of the most important acquisitions made during the Jimmy Johnson era, helping to solidify the team's defense along with Charles Haley.
In 1995, he was limited to 13 games (10 starts) because of a knee injury, registering 60 tackles, 4 passes defensed, one fumble recovery and one sack.
[8] His brother Eric Everett played for the Philadelphia Eagles (1988–89), Tampa Bay Buccaneers (1990), Kansas City Chiefs (1991), and Minnesota Vikings (1992).