Curtis has previously written and directed "Love Actually" and penned "Bridget Jones's Diary".
"About Time" is a fantastical feel-good movie about a man and his ability to travel back in time. He eventually meets the girl of his dreams, said The Hollywood Reporter.
Domhnall Gleeson, son of actor Brendan Gleeson, will play the male lead. Bill Nighy, Tom Hollander, Margot Robbie, Lydia Wilson and Vanessa Kirby are set to co-star.
Production is set to begin in London in June. Working Title's Tim Bevan, Eric Fellner, Liza Chasin and Amelia Granger are producing the film.
McAdams will next appear in theatres in Terrence Malick's untitled latest project, whose all-star cast also includes Ben Affleck, Javier Bardem and Rachel Weisz.
