Gaydosh was ranked as the 2nd best player in the Canadian Football League's Amateur Scouting Bureau final rankings for players eligible in the 2013 CFL Draft. He ranked 3rd best in both the December and April (final) rankings. Gaydosh had arguably the best performance of the 2013 CFL Combine. Duane Forde said that, "If rankings were based solely on the combine Linden Gaydosh would be the number one guy.".
On May 12, 2013, less than a week after being drafted into the CFL, Gaydosh signed with the Carolina Panthers of the National Football League. On August 2, 2013, Gaydosh was waived/injured by the Carolina Panthers due to a back injury. On August 3, 2013, Gaydosh cleared waivers and was placed on the injured reserve list. He spent the entire 2013 NFL season on the injured reserve. He was released by the Panthers on August 24, 2014; prior to the 2014 NFL season.
On September 4, 2014, Gaydosh signed with the Hamilton Tiger-Cats (who held his CFL rights). He appeared in nine regular-season games, registering four tackles, two tackles for a loss and a pass knockdown. He added four tackles in two playoff contests. During an off-season workout in the spring of 2015, Gaydosh tore his Achilles tendon, which required surgery and caused him to miss the 2015 season. He returned to Hamilton in 2016, making appearances in both pre-season games and the season opener against Toronto.
On August 6, 2017, Gaydosh signed with the Toronto Argonauts. Gaydosh played in 11 games for the Argos during the 2017 season, and went on to win the 105th Grey Cup. Gaydosh played in 14 games for the Argos in 2018, and was signed to a contract extension following the season.