A lifelong Hammers fan, the club said he passed away "peacefully" on Wednesday morning with his fiancee and daughters by his side.
Gold, previously the chairman and co-owner of Birmingham City, became joint-chairman at West Ham with David Sullivan in 2010.
"I am extremely sad to hear this news," said manager David Moyes.
"On behalf of all of the players and my staff at the training ground, I would like to extend our deepest sympathies to David Gold's family at this very difficult time.
"Mr Gold was a regular visitor to Rush Green and always a source of great support and encouragement to myself and the players.