Jay Z has previously been involved in producing a number of movies, including the Annie remake, Top Five and The Great Gatsby.
Company co-chairman Weinstein said: "Having known Jay on a personal level for many years we are thrilled by the opportunity to expand our relationship. Jay's ability to influence entertainment and pop culture has gone well beyond music for many years.
"He approaches every aspect of his career with both determination and effortlessness, making him one of the leading power players in entertainment history. We already have some exceptional projects in the works and are excited to see what more is to come."
And president and COO Glasser added: "Jay Z is an entertainment mogul with an unparalleled sense of the industry and limitless creativity.
It's an incredible opportunity to be able to collaborate with him as we continue to grow our TV division and look towards many more opportunities to create fresh content."
Jay Z, 46, is already involved in the worlds of sports, music and fashion, through his Roc Nation company.