The Swede won the race to succeed Angelina Jolie, who played Lara Croft in two previous films tracking the fictional adventurer, who started life as a video game heroine in 1996.
The film will be co-produced by MGM and Warner Bros, crowning a period of remarkable success for the 27-year-old Vikander.
She won an Oscar in February for The Danish Girl, becoming the first Swedish actor to scoop an Academy Award since Ingrid Bergman in 1974. She was was also nominated for Golden Globe and Bafta awards for her gripping performance in the British sci-fi psycho-drama Ex Machina.
The Swedish star has also scored a role in the upcoming 'Jason Bourne' sequel, which will see Matt Damon return to the big screen as the amnesiac super spy.
If Vikander misses Scandinavia while on the set of Tomb Raider she won't have to look far for a chat: Norway’s Roar Uthaug has been lined up to direct.
Born in Sweden's second city of Gothenburg in 1988, Vikander initially dreamed of becoming a ballerina, studying at the Royal Swedish Ballet School in Stockholm before injuries cut her dance career short in her teens.
Her focus then turned to acting, and her on-screen career gained traction after appearances in Swedish short films and the popular television drama series 'Andra Avenyn' from 2008 to 2010.
Vikander accepting her Oscar for best supporting actress. Photo: Chris Pizzello/Invision/AP