The Hollywood Reporter said Lesher will be replaced by production President Adam Goodman, who Grey expressed extreme confidence in following Friday's dismissals.
"Adam has proven himself to be a terrific executive with a track record of having shepherded some incredibly successful films," Grey said. "We have worked closely with Adam over the last few years and look forward to expanding his duties."
No replacement for Weston was reported.
Despite the firing of Lesher and Weston, Paramount has offered both executives production deals.
The Hollywood Reporter said the shakeup came as Paramount has enjoyed strong success with hits such as "The Curious Case of Benjamin Button" and "Star Trek." The studio also has "Transformers: Revenge of the Fallen" on deck for release next week.
Celebrity Families of 2014 [PHOTOS]