Drawn up in collaboration with local architect NBBJ, the $1 billion (£0.6 billion) scheme will create eight new soundstages for Silvercup Studios Associates - the home of hit television shows such as The Sopranos.
The 185,000m 2project, one of three high-profile jobs Rogers is working on in New York, will also include 1,000 new homes, offices and 'cultural spaces.'
He has been asked to design one of the new towers at the World Trade Center site, as well as the Jacob K Javits Convention Center.
The Silvercup studio project, which overlooks the East River south of Queensboro Bridge, won the go-ahead last week from New York City Council following recommendations from the City Planning Commission, borough president and local community board.
A key element of the development will be the restoration of the New York Architectural Terra-Cotta Company building, a local landmark built in 1892.
Rogers said: 'We are extremely pleased that the scheme for Silvercup West has achieved planning approval. The design will allow public access to an area of the East River waterfront in Queens, which has previously not been accessible.
'It will be a pivotal scheme supporting future developments from Long Island City central business district to the river.'