Wesslau is a product of AIK, a club near the capital city of Stockholm. He represented his country at all youth team levels from U16 to U20 and made his debut on AIK's men's team during the 2003-04 season. He later played for other teams of the first and second division in Sweden, including the Malmö Redhawks, Almtuna IS, Borås HC and Djurgårdens IF.
Wesslau returned to Djurgården on May 2, 2011 [3] and later signed a three-year deal with HV71 in 2012.[4]
At the conclusion of his contract with HV71, having appeared in 132 regular season games as the club's starting goaltender, Wesslau left as a free agent to sign a one-year contract in Germany with Kölner Haie of the Deutsche Eishockey Liga (DEL) on March 26, 2015.[5] In December 2015, he was handed a contract extension through 2018.[6] He received 2016-17 DEL Regular Season Goaltender of the Year honors.[7]