He was an Australian Institute of Sport scholarship holder, and in 2010 he became the Under 23 Road Race World Champion.

Matthews left Rabobank at the end of the 2012 season, and joined Orica–GreenEDGE on a two-year contract from the 2013 season onwards. In 2015, Matthews won the points classification jersey of Paris–Nice as well as a stage. He won third place in the 2015 Milan–San Remo. He also met success at the opening stage of the Tour of the Basque Country by outsprinting a group of about fifty riders after a hilly day. He then went on to a second place in the Brabantse Pijl, winning the sprint of the group after nearly getting to lone escapee Ben Hermans. At the Amstel Gold Race, Matthews grabbed another notable result, while he came in third of the final dash for the line while being part of a small leading group. At the Tour de Suisse, Matthews won stage 4 after following Peter Sagan's wheel in the sprint and passing him in the final meters (yards).

He was named in the start list for the 2015 Tour de France. In the 2016 Tour de France, Matthews out-sprinted a breakaway group of 7 riders to win stage 10, his first stage win in the Tour de France, completing a set of Grand Tour stage victories.

In August 2016 it was confirmed that Matthews would join Team Sunweb for the 2017 season.

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