Woodley, a three-year letterwinner, was part of a two-quarterback system with Steve Ensminger under late head coach Charles McClendon from 1977-79, taking the Tigers to three consecutive bowls in the final years of Coach McClendon's distinguished tenure at LSU. The Tigers went to the Sun Bowl in 1977, the Liberty Bowl in 1978 and the Tangerine Bowl in 1979, winning 23 games in those three seasons.
It was the senior quarterback from the city which had a reputation at that time of developing quarterbacks who had a big hand in that 34-10 win over Wake Forest in the 1979 bowl as he scored twice in the first quarter on rushes of 13 and three yards and then completed a 50-yard pass to Carlos Carson and a 19-yard touchdown throw to Jerry Murphree to give LSU a 21-0 lead with 3:28 to go in the first half as LSU won the Tangerine Bowl, 34-10.
In his LSU career, Woodley completed 151-of-310 passes for 2,081 yards and eight touchdowns. The product of C. E. Byrd High School was at 6-2 and with 4.6 speed a valuable asset to LSU as a running quarterback as well and in his four years he rushed for 833 yards and 15 touchdowns.
After his LSU career, Woodley went on to play five seasons in the NFL, four with the Miami Dolphins and one with the Pittsburgh Steelers. He was the starter for the Dolphins in Super Bowl XVII, leading Miami to a 17-10 halftime lead over the Washington Redskins, before the Redskins rallied in the final 10 minutes for a 27-17 victory.
In his four seasons in Miami, Woodley threw for 5,928 yards and 508 completions. He holds the Miami rookie record for most past completions (176), ahead of both Dan Marino (173) and Bob Griese (166).
Woodley moved back to Shreveport in 1990 and underwent a successful liver transplant in 1992. One of his last public events he participated in the Shreveport area was this past season when he served as the color commentator on the radio broadcasts of his alma mater, Byrd. He was inducted into the school's Hall of Fame in 1995.
Six brothers and sisters survive him.