Principal photography started last month in New Orleans, then shifted to London from July 27 to Sept. 26.
Cast includes Uma Thurman, Sienna Miller, Daniel Bruhl, Riccardo Scamarcio, Emma Thompson, Lily James, Omar Sy, Jamie Dornan, Sam Keeley, Sarah Greene and Alicia Vikander.
John Wells is directing with a screenplay by Steven Knight. Stacey Sher, Michael Shamberg and Erwin Stoff are producing.
Cooper will play a chef in Paris who only ever cared about the thrill of creating explosions of taste and wants to obtain the Michelin three-star rating. Rhys will play a rival chef who stands in the way.
Rhys is repped by WME and Management 360 in the U.S., and United Agents in the U.K. News was first reported by Deadline.com.