Gostisbehere played college hockey with the Union Dutchmen in the NCAA Men’s Division I ECAC Hockey conference. In his junior year, Gostisbehere’s outstanding play was rewarded with a selection to the 2013–14 ECAC Hockey All-Conference First Team. The Dutchmen won the national title in 2014 and Gostisbehere earned great praise for his three points and plus-7 performance in a 7–4 win over the Minnesota Golden Gophers.

On April 15, 2014, Gostisbehere was signed by the Flyers to an entry-level contract. However, Gostisbehere suffered a torn ACL in November that kept him out of the lineup for the rest of the 2014–15 season in which he was slated to play for the Lehigh Valley Phantoms.

Gostisbehere impressed in training camp preceding the 2015–16 season, but was ultimately sent down to the Phantoms. A month into the season, on November 14, 2015, Gostisbehere was called up by the Flyers, and recorded his first career NHL point in his opening appearance with the Flyers on a game-tying assist against the Carolina Hurricanes. Three days later he scored his first NHL goal against Jonathan Quick of the Los Angeles Kings and followed it up with two overtime winners which were described as “absolutely identical”, making him the first Flyers rookie to score multiple overtime winners in a season. Gostisbehere later added a third overtime goal against the Carolina Hurricanes, marking the second time that he’d scored the overtime winner against Carolina.

On February 13, 2016, he broke Barry Beck’s point streak record for a rookie defenseman with a goal against the New Jersey Devils, extending his streak to 11 games. On February 20, 2016, he extended his point streak to 15 games with an overtime goal against Toronto. Gostisbehere became the first rookie in NHL history to record 4 OT goals in a season. On February 23, 2016, his point streak ended at 15 games in a loss against the Carolina Hurricanes.

On June 9, 2017, Gostisbehere signed a six-year, $27 million deal with the Flyers, worth $4.5 million a season.

Following a 4-1 defeat to the Florida Panthers on March 4, 2018, Gostisbehere invited the hockey team of Marjory Stoneman Douglas High School to a meet and greet. This was weeks after the Stoneman Douglas High School shooting.