According to his family, Grey has been battling cancer for quite some time.
Grey, who succeeded Sherry Lansing, stepped down as CEO of Paramount in February.
He also co-founded Plan B Entertainment with Brad Pitt and Jennifer Aniston, through which he produced "The Departed".
Grey joined Paramount in 2005 and during his tenure the studio produced or distributed hit films including "Transformers: Dark of the Moon", as well as the "Star Trek" and "Mission Impossible" franchises.
Sumner and Shari Redstone, in a joint statement noted how Grey's "tremendous kindness and talent inspired so many of us in the entertainment industry". He was always good to me, in the small passing moments we had.
Born in NY in 1957, Grey started out in the entertainment business as an assistant to Harvey Weinstein, who was then a concert promoter. "Kind & classy and a helluva boss".
Grey also brought Scorsese into his Paramount circle with an overall deal that resulted in such films as Shutter Island (2010), Hugo (2011), The Wolf of Wall Street (2013) and last year's Silence.
"Oh man the world has lost a gentleman", Chu wrote on Twitter. And as he tracked new comics, he discovered his first client, the comedian Bob Saget.
Those in Hollywood who knew him paid their respects, including director James Gunn. "He was a thoughtful partner on "Just Shoot Me" and remained a friend".
Grey is survived by his wife, Cassandra, their son, Jules; three grown children - Sam, Max and Emily - from a previous marriage to Jill (nee Gutterson) Grey; his mother, Barbara Schumsky, and siblings Michael and Robin.