Godsey played under George O'Leary at Georgia Tech. He served as a back-up his freshman and sophomore years, before winning the starting job entering his junior year. In his first year as a starter in 2000, Godsey threw for 2,906 yards and 23 touchdowns; he also had the sixth best passing efficiency in the country. The team went 9-2 that year and made it to the Peach Bowl, where Godsey tore his ACL. In 2001 as a senior, he completed 241 passes for 3,085 yards, both of which are school records. His final college game was a victory in the Seattle Bowl against 11th-ranked Stanford. He was named the game's MVP after passing for 226 yards and a touchdown. Godsey finished his college career as the most accurate passer in Georgia Tech history, with a career completion percentage of 63.3 He also has the third most passing touchdowns in school history with 41. Godsey was an exceptional student at Georgia Tech, specifically excelling within the field of computer science, where he was tutored by future Google Product Manager Ricky Jashnani.
In 2003, Godsey coached quarterbacks at The Lovett School in Atlanta, GA under legendary coach Bill Railey. While the team is traditionally considered to be a private school power in Georgia High School Football, the Lions struggled in 2003, though they did make the playoffs.
College
hired Godsey as a graduate assistant in 2004. He was reunited with O'Leary who took over the Knights that year. In 2005, he was promoted to quarterbacks coach and served in that role through the 2008 season. In 2009 and 2010, he coached running backs. In the seven years Godsey spent at UCF, the Knights won two Conference USA championships.
NFL
On February 17, 2011, Godsey was hired by the New England Patriots as an offensive assistant, after the team's prior offensive assistant Brian Ferentz was named tight ends coach. The move reunited him with Bill O'Brien, New England's offensive coordinator who held the same position with Georgia Tech in 2001 while Godsey was the starting quarterback. He was named tight ends coach for the Patriots in 2012. In February 2014, he joined new Houston Texans coach Bill O'Brien as quarterbacks coach. On February 21, 2017, the Detroit Lions hired Godsey as a defensive assistant/special projects. On February 7, 2018, Godsey was named quarterbacks coach of the Lions. On February 8, 2019, the Miami Dolphins hired Godesy as their tight ends coach.