Morrison was born in Lima, Ohio. He attended the University of Cincinnati where he played both halfback and quarterback and also played on defense during his three varsity seasons. Morrison was drafted by the Giants in the third round of the 1959 NFL Draft, where he mostly played at the positions of running back and wide receiver. He had a long career with the Giants, playing from 1959 to 1972. He is 3rd on the Giants' team record for receptions, with 395 catches, from seven different quarterbacks; over his career his plays gained 4,993 yards. His jersey number (#40) has been retired by the Giants.