A spokeswoman for Wilde confirmed that the couple are engaged. The engagement was first reported by People.com.
This will be the second wedding for both actors.
Wilde finalised her divorce from Tao Ruspoli in 2011 after eight years of marriage.
Sudeikis was previously married to Pitch Perfect screenwriter Kay Cannon. They divorced in 2010.
Wilde, 28, rose to fame on TV's House. Her film credits include Tron: Legacy and Cowboys & Aliens.