Director Christopher McQuarrie announced the new cast members on Thursday via Instagram.
Actor Greg Tarzan Davis have also joined the film, which has been shot through 2020 and 2021 amid the pandemic.
The details of the roles of the new cast members aren''t clear, but in photographs McQuarrie posted to Instagram, Delaney can be seen wearing a military uniform, and Elwes'' photo had a caption â€œWelcome to The Community.â€
The actors join returning stars Vanessa Kirby, Rebecca Ferguson, Ving Rhames, Simon Pegg, Angela Bassett and Henry Czerny, as well as newcomers Pom Klementieff, Hayley Atwell, Shea Whigham and Esai Morales.
Paramount Pictures will be releasing "Mission: Impossible 7" in theatres this year in November.