The resignation comes as his role in the aftermath of the 1989 Hillsborough disaster is being investigated.
At the time of the tragedy he was a South Yorkshire Police inspector who attended the match as a spectator and later took part in an internal inquiry.
West Yorkshire Police Authority said media attention and the investigation by the police watchdog were “proving to be a huge distraction for the force”.
Sir Norman has been referred to the Independent Police Complaints Commission over allegations he provided misleading information after the disaster, in which 96 Liverpool fans died.
His resignation comes after candidates bidding to become West Yorkshire’s police and crime commissioner called for him to stand down now rather than retire in March as planned.
In a statement, Sir Norman said: “The police authority, and some of the candidates in the forthcoming PCC elections, have made it clear that they wish me to go sooner.
“I do so, not because of any allegations about the past, but because I share the view that this has become a distraction to policing in West Yorkshire now and in the future.”