Finley played for the Edina Peewee A state championship team in 1999–2000. Finley was a standout playing Minnesota High School hockey for the Edina Hornets. Due to Finley's strong play and leadership his freshman year, he made the White line the following year. In 2005, he said that making the White Line may well have been the greatest accomplishment of his hockey career. Finley missed the majority of the 2009–10 season on injured reserve when on November 21, 2009, in a game with the Stingrays against the Gwinnett Gladiators, he ruptured an artery in his hand which required surgery. On September 18, 2011, Finley accepted an invitation to training camp by the Buffalo Sabres. He impressed enough that he was signed to an AHL contract, and assigned to the Rochester Americans. Through the first quarter of the season, Finley was impressive as one half of the Americans shut-down defensive pairing. He led the Amerks in +/- with a +10. The Sabres and Finley reached a three-year contract on November 28, 2011, that will allow Finley to be called up by Sabres organization. Two days after the deal was completed, Finley was called up by the Sabres where he made his NHL debut against the Red Wings on December 2, 2011. Finley was the 475th player to play in the NHL after starting his career in the ECHL. Prior to the lockout shortened 2012–13 NHL season, Finley was claimed off waivers from the Sabres by the New York Islanders on January 14, 2013. On July 29, 2014, Finley signed as a free agent to a one-year AHL contract with the Hamilton Bulldogs. In the 2014–15 season, Finley appeared in 54 games with the Bulldogs, contributing with 3 assists and 132 penalty minutes. On October 8, 2015, Finley continued in the AHL, signing a one-year AHL deal with the Iowa Wild, an affiliate to the Minnesota Wild. In the 2015–16 season, Finley appeared in 56 games with Iowa, recording a professional high of 5 goals from the blueline. On June 21, 2016, Finley opted to pursue a career abroad, agreeing to a one-year deal with Finnish club, HIFK, of the Liiga. On February 3, 2017, HIFK announced a two-year contract extension with Finley.
