Strome has two brothers who also play hockey, Dylan and Matthew. Dylan currently plays in the National Hockey League with the Chicago Blackhawks organization. The youngest brother Matthew was drafted by the Philadelphia Flyers in 2017. The Strome family had been dubbed as the future Sutters and Staals, families where multiple siblings have gone on to successful ice hockey careers. The Strome brothers grew up in the Lorne Park area of Mississauga.