The Bulls fan replaces Ken Kinnersley, who recently he was to retire earlier this summer.
He says his is proud to lead the National League North club forward - and is well aware he has a lot to live up to.
Graham told the club’s website: “I am honoured and immensely proud to be appointed chairman of this football club.
“This is a club, city and community I love, and I’m humbled that my fellow board members have chosen me for this role. I’m hugely grateful for their support.
“Hereford Football Club has been created and funded by fans, and I believe it is owned by everyone who supports the club. It survives through the dedication and commitment of its supporters.
“One such devoted volunteer is outgoing chairman, Ken Kinnersley. Ken’s contribution has been well referenced already, but I must add that he has contributed much more than any words he has ever felt the need to share externally.
“As a Hereford fan myself, it has been clear to see, and experience, his undoubted passion for the club and his resilience in his efforts to make it a better place for us all.
“Personally, I would like to thank him for the important role he has fulfilled.
“No-one should ever underestimate the vital role Ken has played in Hereford FC’s journey. He has always acquitted himself professionally, with truly honourable intentions.
“I am in no doubt that I have huge shoes to fill.”