People.com reported the news Wednesday, but did not offer any details regarding how the couple got engaged or when they plan to wed. They have been dating for about three years.
Tamblyn, 28, starred on TV's "General Hospital," "Joan of Arcadia" and "House," as well as "The Sisterhood of the Traveling Pants" films.
Cross, 47, is best known for his work on the small-screen comedies "Arrested Development" and "The Increasingly Poor Decisions of Todd Margaret."
Celebrity Couples of 2014 [PHOTOS]