Stroma was born in London, England, to father Stefan Sjöström, a Swedish-born computer industry executive, and German mother Crystal Sjöström, and grew up in Ascot, England in Berkshire, about 25 miles west of London. He was educated at the public boys-only boarding school Radley College in Oxfordshire, leaving in 2005. He has an older sister, Antonia Sjöström, and a younger brother, Philipp Sjöström.

When he was 16, Stroma was accepted to the National Youth Theatre of Great Britain. He had roles on various British TV shows, including Casualty and BBC’s detective show, Mayo (aka The Gil Mayo Mysteries). While studying neuroscience at University College London, Stroma continued to work as an actor and model. He ended up taking a year off from university to play the role of Cormac McLaggen in Harry Potter and the Half-Blood Prince. After filming was over, Stroma completed his degree at University College London. In 2009, he attained a 2:1 BSc (an upper-second-class degree) in Neuroscience.

In 2014, he was cast in the role of Jack in the psychological thriller After the Dark, which was formerly known as The Philosophers, with his former Harry Potter co-star Bonnie Wright. The film was shot on location in Jakarta.

In June 2015, Stroma was one of the romantic interests, Adam Cromwell, in the Lifetime dramedy Unreal. He plays British bachelor who is competing on a fictionalized The Bachelor-type reality show called Everlasting. Stroma’s character is manipulated as much as the women who are vying for his attention in the show that is a behind-the-scenes view of reality dating shows.

In 2016, he joined the cast of the HBO series Game of Thrones in Season 6 as Dickon Tarly, the brother of Samwell Tarly.

Stroma began dating his Unreal co-star Johanna Braddy in the summer of 2015. Stroma and Braddy got engaged in May 2016, and were married on 30 December 2016, in Atlanta, Georgia.