Arcel was born and raised in Copenhagen. His mother, Libby Tata Arcel, is a psychologist from the Greek city Mytilene, on the island of Lesbos, while his father, Arne Arcel, is an architect from Denmark. His parents divorced when he was seven. His elder sister is actress Nastja Arcel. He attended Bernadotte School in Hellerup and secondary school at Øster Borgerdyd Gymnasium. He then enrolled at the National Film School of Denmark from where he graduated as film director in 2001. His graduation project, the short film Woyzeck’s Last Symphony, won the Grand Prix at Clermont-Ferrand International Short Film Festival.

Arcel made his debut in 2004 with the political thriller King’s Game, which won him the award for Best Director at the Danish Film Academy Awards. It was followed by the adventure film Island of Lost Souls in 2007 and the generational comedy Truth About Men in 2010.

After experiencing an international breakthrough with A Royal Affair, he moved to Hollywood to pursue a career in filmmaking there. He directed the film adaptation of Stephen King’s The Dark Tower. The film began principal photography in early 2016 and was released on 4 August 2017.