After redshirting his first year at Boise State in 2013, Finley played in five games in 2014, completing 12 of 27 passes for 161 yards with two touchdowns and an interception. He was named the starting quarterback for Boise State his redshirt sophomore year in 2015. He played in three games before suffering a season-ending ankle injury. In the three games, Finley completed 46 of 70 passes for 455 yards, one touchdown and four interceptions.
After the season he transferred to NC State University. In his first season at NC State, he completed 243 of 402 passes (60.4%) for 3,059 yards, 18 touchdowns and eight interceptions.
In Finley's redshirt junior year, he completed 312 of 479 passes (65.1%) for 3,518 yards, 17 touchdowns, and 6 interceptions. He also rushed 69 times for 194 yards and 3 touchdowns and caught 2 passes for 18 yards. He was also named to the Academic All-ACC team for earning a 3.889 GPA.
Finley was drafted by the Cincinnati Bengals in the fourth round (104th overall) of the 2019 NFL Draft. He currently is in contest with other Bengals' quarterback Jeff Driskel competing for Andy Dalton's backup position, and appears to have the upper hand. Finley finished the preseason completing 34 of 46 pass attempts for 305 yards with two touchdowns and no interceptions.