The 27-year-old star beat favourite Kate Winslet for the award. The Steve Jobs star was seen as the frontrunner after winning both the Bafta and Golden Globe for her performance. Vikander had also won the Screen Actors Guild award for her role.
The film, directed by Oscar-winner Tom Hooper, focuses on the first ever recipient of gender reassignment surgery and the effect this has on his marriage. Vikander stars opposite Eddie Redmayne, who is also nominated for his performance.
It was one of many films last year to star the Swedish actor. Vikander also appeared in foodie drama Burnt, period action comedy The Man From UNCLE, sci-fi thriller Ex Machina, fantasy adventure Seventh Son, crime thriller Son of a Gun and wartime romance Testament of Youth.
She will next be seen opposite Matt Damon in franchise reboot Jason Bourne, with Judi Dench and Jack O’Connell in romance Tulip Fever, and alongside real-life partner Michael Fassbender in The Light Between Oceans.
