He was known for roles in the Thor films and the Divergent series, as well as several UK TV shows like Band of Gold, Peak Practice and Murphy's Law.
His US-based publicist firm, Viewpoint, confirmed his death to the BBC but did not provide any further details.
No cause of death has been revealed but he was reportedly hospitalised during filming on the Italian island Ischia.
At the time of his death, he was working on an action movie, Cassino in Ischia.
His death was announced four days before his 59th birthday.
Stevenson was born in Northern Ireland but moved to England when he was eight years old.
His father was stationed with the Royal Air Force (RAF) near Lisburn, County Antrim, at the time of his birth in 1964.
His family relocated to Newcastle upon Tyne and he spent much of his childhood in England.
Stevenson was inspired to become an actor after seeing John Malkovich in a play at a West End theatre in London.
He studied acting at the Bristol Old Vic Theatre School and one of his first TV roles was in the Catherine Cookson drama The Dwelling Place.
He later appeared in a wide range of British TV shows including Waking the Dead, Dalziel and Pascoe and At Home with the Braithwaites.
In 2004, he played a knight in the big-budget Hollywood film, King Arthur, which starred Keira Knightley.
More recently, Stevenson secured roles in successful US-made TV shows and movies, taking the role of Volstagg in the Thor trilogy and Titus Pullo in HBO's historical drama series Rome.
He will star as Baylan Skoll in the upcoming Disney+ series Star Wars: Ahsoka.