Covert was chosen in the first round of the 1983 NFL Draft (sixth overall) by the Chicago Bears and head coach Mike Ditka, himself a former Pitt All-American from Western Pennsylvania. "Jimbo's the guy we wanted. From Day 1, we put him at left tackle and moved on," Ditka said. "You don't get too many people who come along who can make that impact. He had the respect of all his teammates and all his coaches."
During Covert's career, he was named to an All-Pro team three straight years (1985–1987), a first- or second-team All-NFC selection four times (1985–1987, 1990), and a first- or second-team All-NFL selection three times. Covert was a consensus All-NFL and All-Pro pick in 1985 and 1986. He was selected to two Pro Bowls, in 1985 and 1986. In 1985 he was selected as the NFC's offensive lineman of the year and in 1986 he was selected as the Miller Lite NFL Offensive Lineman of the Year.
In 1990, the Pro Football Hall of Fame Board of Selectors selected Covert to the NFL All-Decade Team. With Covert on the team, the Bears won six NFL Central Division titles and played in three NFC Championship games, along with the Super Bowl win.
Covert was inducted into the Beaver County Sports Hall of Fame in 1996, the College Football Hall of Fame in 2003, the National Italian American Sports Hall of Fame in 2004, the Western Pennsylvania Interscholastic Athletic League Hall of Fame in 2009, the Pennsylvania Sports Hall of Fame in 2012. He had been nominated for the Pro Football Hall of Fame on numerous occasions. On January 15, 2020, Covert was elected to the Pro Football Hall of Fame Centennial Class of 2020.