The statement said that he died "peacefully this morning surrounded by his family after a brief illness".
Stewart became a regular face in British households in the late 1980s for hosting the popular Channel 4 general knowledge quiz programme, which he also produced.
He fronted the show, dubbed one of the toughest quizzes on TV, from its inception in 1988 until 2003.
The series was revamped in 2013 for a celebrity special hosted by comedian Adam Hills, and in 2014 returned for a new series with Sandi Toksvig as presenter.
Stewart was also known for being the producer and director on game shows The Price Is Right and Family Fortunes, and sitcom Bless This House, among others.
In 1997 Stewart married his third wife Laura Calland, a voice-over artist for Fifteen To One.