Wellman was born on July 15, 1956, in Newton, Kansas.[1] He was the son of Vere Wellman, a football coach.[2] He attended Lawrence High School and competed in football as well as in track and field.[3] He was the fifth Lawrence alumni to make it to the NFL.[4]
Wellman was selected in the third round (81st overall) of the 1979 NFL draft by the Los Angeles Rams.[13] He was traded to the Green Bay Packers in exchange for a middle round 1981 draft pick in August 1979 after the Packers were "desperate" for a center.[14] He was one of nine rookies to make the 1979 Packers squad.[14] He made his NFL debut in a 6–3 loss to the Chicago Bears and ended up playing all 16 games for the team in 1979.[15]
Wellman was a backup to Larry McCarren and saw little playing time, however; an article from United Press International (UPI) noted that he "sat, sat, sat" and that "[e]xcept for an occasional long snap with the Packers, Wellman's career has been punctuated by clean pants."[8] His only statistic recorded in 1979 was a 10-yard kickoff return.[1] Wellman returned to the Packers in 1980 and made the team, but was placed on injured reserve after four games with an undisclosed non-football illness.[5][16] He was released by the team on October 30, 1980.[17]
After being released by the Packers, Wellman considered retiring, but then "spent more hours in the weight room ... than ever before" in an attempt to return to the NFL.[8][18] He was signed by the Kansas City Chiefs on April 2, 1981.[17] He was waived, however, on August 18 that year.[19] Wellman then tried to make the Edmonton Eskimos of the Canadian Football League (CFL) for the 1982 season but did not make the team.[20] He had a comeback attempt in 1983 with the San Francisco 49ers, but was released in August of that year after having been signed in June.[17][21][22] He then signed with the team again on July 22, 1984, only to be released on August 8.[23][24] He finished his professional career with 20 games played, none as a starter.[5]