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"They are absolutely thrilled and looking forward to the new addition to their young family," her rep tells PEOPLE.
The actress, 26, and her actor/musician husband, Nathan West, are already parents to two children.
Leigh's pregnancy will not be written into the Grey's storyline, according to her rep Marcel Pariseau.
Leigh plays "Lexie," the half sister of Meredith (Ellen Pompeo) on ABC's hit medical program. She joined the show in July 2007.
Before Grey's, Leigh previously starred in the short-lived series Reunion and That 80s Show. She also starred in 2001's Not Another Teen Movie.
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