He was selected fifth overall in the 2011 NHL Entry Draft by the New York Islanders and began playing with the team during their 2013–14 season.

[4][5] After his second season with the IceDogs, Strome became eligible for the National Hockey League (NHL) Entry Draft.

Halfway through the following season, on December 11, 2013, he was called up to the Islanders after the team had put Pierre-Marc Bouchard on waivers to make room on their roster.

[11] Following the trade, Oilers coach Todd McLellan praised Strome's versatility and ability to play many roles on the ice.

[12] Prior to the start of the 2017–18 season, Strome was expected to play on Connor McDavid's right wing or be the second- or third-line center.

[13] As the month of October continued, Strome often played on the right wing of the second line with Ryan Nugent-Hopkins and Milan Lucic.

[16] While playing on this line, Strome tallied the Oilers 10,000th goal in team history during their 5–3 win over the San Jose Sharks on December 18.

[17] His production eventually slowed down and he became a mainstay on the Oilers third line between Jujhar Khaira and Michael Cammalleri.

As a restricted free agent in the off-season, Strome agreed to two-year, $6.2 million extension with the Oilers on July 6, 2018.

[33] On March 23, he tallied his first career overtime goal to lift the Rangers to a win over the Toronto Maple Leafs.

Strome began the season strong, earning top playing minutes with linemate Artemi Panarin after Mika Zibanejad suffered an upper-body injury.

[44] Following his fourth season within the Rangers organization, Strome left as a free agent and was signed to a five-year, $25 million contract by the Anaheim Ducks on July 13, 2022.

[47] Despite failing to produce on the powerplay, Strome maintained a five game point streak to begin the season, tallying one goal and eight assists over that stretch.

The youngest brother Matthew was drafted by the Philadelphia Flyers in 2017, and currently plays on the American Hockey League's Hershey Bears.