The actress will play a young doctor on the ABC medical drama, reports Deadline.
Luddington notably played Kate Middleton - now the Duchess of Cambridge - in William & Kate, a Lifetime movie charting Middleton's relationship with Prince William before their marriage.
She has also appeared in HBO's vampire drama True Blood as Claudette and played a nanny in a multi-episode arc on Showtime's Californication.
Luddington will voice Lara Croft in the new Tomb Raider reboot, which is due out next year. She is also providing motion capture for the character.
Describing the role as an honour, she said: "People love Lara and there is such a huge fanbase that you don't want to disappoint."
Grey's Anatomy will return to ABC later this year.