The book depicts Brian Clough's fiery 44-day reign at Leeds United in 1974 and other key roles in the £10m film will see Michael Sheen play Clough, Colm Meaney as Don Revie and Timothy Spall as Peter Taylor.
Graham has made a name for himself playing hardcases, notably as Combo in the film 'This Is England'.
He has reported to have been practising a Scottish accent ahead of filming and said: "I'm made up about it. I've got the wig to look like Billy. I'm doing football training too. He was a proper legend."