Brockington was the Green Bay Packers 1st round draft choice, the ninth selection overall, in 1971. He was the first NFL player to ever rush for 1,000 or more yards in each of his first three seasons. In 1971 Brockington was named The NFL Offensive Rookie of the Year by the Associated Press. Brockington was named All-Pro in 1971, 2nd Team All-Pro in 1973 and All-NFC in 1972. He was also selected to 3 consecutive Pro Bowls (1971-1973).