Snider has guided Universal's development and film production since 1999 and her departure will leave a major hole it its executive ranks, The New York Times reported.
Snider's decision to move over to DreamWorks is part of Paramount's strategy to revitalize the studio currently run by David Geffen and Steven Spielberg.
"It's what we talked about from the get-go, bringing the best and brightest to Paramount, both in front of and behind the camera," Paramount Chairman Brad Grey said in making the announcement Sunday. "Stacey is an extraordinary and unique piece of talent as an executive."
Snider and Geffen will work together on four to six movies a year, with an estimated budget of $85 million per film, the Times said.