"They are incredibly happy," a source close to the pair tells People. "They're very excited to welcome a new member into their family."
Wilde, 29, and Sudeikis, 38, met in 2011 when Wilde made a cameo onSaturday Night Live. They took their relationship public in 2012 and announced their engagement in 2013.
Wilde tweeted Sunday: "WOW. You guys are awesome. So kind. Thank you thank you thank you! PS. Babies eat mostly salsa right?"