The team didn't specify a cause of death.
Coach Wilson was 60 years old.
Wilson was the Bears quarterbacks coach from 2004-06 as their passing game improved from the worst in the NFL to above league average.
Originally selected by the Minnesota Vikings in the eighth round of the 1981 NFL Draft (210th overall) out of Texas A&M Commerce, Wilson played in 125 career contests with 69 starts and completed 1,391-of-2,428 passes for 17,283 yards with 99 touchdowns.
He also played for Atlanta, New Orleans, Dallas and Oakland before retiring in 1999.
Dallas Cowboys owner Jerry Jones said in a statement: "This is a sad day for all members of the Cowboys family as we have lost a truly great man".
Wade Wilson of the Dallas Cowboys poses for his 2007 National Football League headshot at photo day in Irving, Texas. That year, Dallas would go on to win Super Bowl XXX and earn him a ring. Prescott's numbers, however, dipped in his second season in 2017.
Wilson's best season statistically was 1988, when he led the National Football League with a completion percentage of 61.4 percent with 15 touchdowns and nine interceptions.
Wilson completed his career with a 75.6 quarterback rating on 1,391-of-2,428 passing for 17,283 yards.
Wilson was replaced by Kellen Moore, who also took over as the position coach for the quarterback he played behind - Dak Prescott.