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.
Central Florida 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.