Graham will take over from Liz Forgan, who has been chair of The Scott Trust since 2003, and will be the seventh to hold the position. He has been a trustee of The Scott Trust since 2012.
After beginning his career at the Bradford Telegraph and The Argus, Graham became a producer at London Weekend Television.
Between 1983 and 1991, Graham worked at Channel 4 as series editor of Diverse Reports and The Media Show.
He set up Wall to Wall in 1987 where he was joint managing director for 10 years, and then chief executive for 16 years. The company won several BAFTAs, Emmys, Royal Television Society and Peabody Awards, and an Academy Award for Man on Wire.
Graham also serves as chair of the Sheffield International Documentary Festival and is a board member of Hampstead Theatre.
The appointment comes during a tough time at the publisher, which in March told staff that it planned to cut 250 jobs. In July, Campaign reported that the Guardian was reducing its media coverage as part of cost-cutting.
Last month, Guardian Media Group revealed in its financial results that it gives "free advertising space" and cash to media agencies in return for adspend.
Graham will take on the post later this year.
Forgan said: "The past 13 years have been an extraordinary period in the life of the Guardian. There will be a proper goodbye from me later but, for now, I am delighted we have appointed a successor who will continue to provide the strong leadership required to guarantee the editorial integrity of the Guardian and a financially sound future for the Guardian Media Group."