The 30-year-old joined the LV County Championship holders as a Kolpak player on a one-year contract subject to clearance from the England and Wales Cricket Board.
Robinson said: "Obviously with the departure of Ryan Harris, we have been keen to bring in a new bowler.
"With his international experience and excellent work ethic, Corey fits the bill perfectly."
Collymore, who has taken 93 wickets in 30 Test matches, added: "The call from Sussex the other day was a very welcome one.
"I've been itching to come over and play county cricket and to be picked by the champions has filled me with confidence. I'm ready to give it my all and can't wait to get started."