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.