Alexander made his acting debut in a Swedish drama film, Åke and His World, which was directed by Allan Edwall.
After some years, he appeared in an American comedy film, Zoolander, which was directed by Ben Stiller. His co-stars of this movie are Owen Wilson, Will Ferrell, Christine Taylor, and Jon Voight. The total budget for this movie is $28 million and made a collection of $60.8 million at the box office.
Later, Alexander appeared in another hit movie, Kill Your Darlings, which was directed by Björne Larson. The co-stars of this movie are Lolita Davidovich, Andreas Wilson, Greg Germann, and Benito Martinez.
After some year, he appeared in an English-language adult animated mystery thriller drama science fiction, Metropia, which was directed by Tarik Saleh.
After his successful career as an actor, Alexander appeared in an American adventure movie, The Legend of Tarzan. The co-stars of this movie are Margot Robbie, Djimon Hounsou, Jim Broadbent, and Christoph Waltz. The total budget for this movie is $180 million and made a collection of $356.7 million at the box office.
Similarly, Alexander also appeared in numerous movies and television series including, The Dog Trick, White Water Fury, The Last Drop, Beyond the Pole, Moomins and the Comet Chase, What Maisie Knew, The Diary of a Teenage Girl, Zoolander 2, Flarsky, Vita lögner, Generation Kill, and Drunk History.
Alexander is a Swedish by nationality and belongs to white ethnicity. Currently, he is in relation to a British model and fashion journalist, Alexa Chung. The couple is dating each other for more than three years. The couple had initially separated following a misunderstanding in their relationship. However, they are back again leading a prosperous life.
Most of Alexander's income comes from her acting and endorsement career. He has appeared in numerous hit movies from which he must have collected a huge amount of salary.
According to some source, his current net worth is estimated to be $12 million. He bought a well-expensive house in Los Angeles for $4 million. He has luxury car A8 which has been manufactured by Audi, and it costs around $70000.