Verhaeghe played minor midget hockey with the Hamilton Jr. Bulldogs before he was drafted 38th overall in the 2011 OHL Priority Selection by the Niagara IceDogs. Following his second season with the IceDogs in 2012–13, posting 44 points in 67 games, Verhaeghe was selected in the third round, 82nd overall in the 2013 NHL Entry Draft by the Toronto Maple Leafs. At the conclusion of the 2013–14 season with the Ice Dogs, Verhaeghe was signed to a three-year, entry-level contract with the Maple Leafs on April 2, 2014. He immediately joined AHL affiliate, the Toronto Marlies, signing an amateur tryout contract to play out the remainder of their campaign. Matching his scoring totals from his previous season with the IceDogs, Verhaeghe scored 82 points as captain in his final season of junior in the 2014–15 season. Prior to his first professional season, Verhaeghe was included in a multi-player trade prior to training camp by the Maple Leafs to the New York Islanders in exchange for Michael Grabner on September 18, 2015. He split the following two seasons between the Islanders affiliates' the Bridgeport Sound Tigers of the AHL and Missouri Mavericks of the ECHL. With one-year remaining on his entry-level contract, Verhaeghe was traded by the Islanders to the Tampa Bay Lightning in exchange for Kristers Gudļevskis on July 1, 2017. In the 2017–18 season with the Syracuse Crunch, Verhaeghe in his first full year in the AHL, secured a top six scoring role scoring a breakout 48 points in 58 games. In the following 2018–19 season, Verhaeghe captured the first AHL scoring title ever by a Crunch skater, claiming the John B. Sollenberger Trophy with 82 points in 76 games. His 34 goals tied Crunch teammate Alex Barré-Boulet in league scoring to share the Willie Marshall Award. Verhaeghe holds the Crunch's single-season total point record with 82 points. On July 5, 2019, Verhaeghe was signed to a one-year, two-way contract extension with the Lightning. On September 30, 2019, the Lightning announced that Verhaeghe had made the team's opening night roster. On October 3, 2019, Verhaeghe appeared in his first career NHL game, which came in a 5–2 Lightning win over the visiting Florida Panthers at Amalie Arena. October 5, 2019, Verhaeghe recorded his first career NHL assist and point in a 3–4 loss to the Florida Panthers at BB&T Center. On December 7, 2019, Verhaeghe recorded his first career NHL goal and first career multi-point game in a 7–1 Lightning win over the visiting San Jose Sharks at Amalie Arena.He scored his first NHL hat trick on January 7, 2020 in a 9–2 win over the Vancouver Canucks.
