On 6 June 2014, despite a contract offer from Oldham, Wesolowski moved to Shrewsbury Town in League Two on a free transfer. He made his debut on the opening day of the season, coming on as a substitute in a 2–2 draw away at A.F.C. Wimbledon, and was a regular in the first team squad until suffering a season-ending injury in a home match against Hartlepool United on 17 January 2015 where he ruptured two knee ligaments. He scored his first and what turned out to be only goal for Shrewsbury in a 2–1 win over Portsmouth on 25 October 2014.