Burgess was a graduate of Colgate University, playing from 1982 to 1985, and was inducted into the Colgate University Athletic Hall of Honor in 1986. As a senior on the 1985 squad, he was named honorable mention Associated Press All-American after setting 14 school records in passing and total offense. He finished ninth in the nation in total offense with 266.1 yards per game. Burgess also received Colgate’s Andy Kerr Trophy, given annually to the squad’s most valuable offensive player. He threw for a school-record 2,565 yards in 1985 and gained a school-record 2,927 yards of total offense.
Tom Burgess was part of a quarterback tandem in Saskatchewan with Kent Austin. Burgess defeated the 16-2 Edmonton Eskimos in the 1989 CFL Western Final replacing an injured Austin who would return to start and with the 1989 Grey Cup. Both quarterbacks were capable starters and Burgess requested a trade in the off-season to pursue a full-time starting opportunity.
Burgess was a full-time starter for the next five seasons. He won a Grey Cup and became an eastern Division all-star selection. He enjoyed a 5,000 yard, 30 TD passing season with Ottawa.
He spent his final two seasons as a Roughrider and was inducted into the Saskatchewan Roughrider Plaza of Honor in 2009.