Wright flashed her engagement ring Friday at the opening of Diane von Furstenberg's "Journey of a Dress" in Los Angeles.
This will be the third marriage for Wright, who was previously married to actor Sean Penn for 13 years.
Wright and Penn share two children, Dylan, 22, and Hopper, 20.
Foster is best known for his work in films “X-Men: The Last Stand,” “Alpha Dog” and most recently, “Lone Survivor,” and has been linked to actresses Kirsten Dunst, Zoe Kravitz and Ellen Page.
"House of Cards" star Robin Wright, 47, and actor boyfriend Ben Foster, 33, are engaged, reports People.