The 26-year-old England international is expected to sign the deal before United's clash with FA Cup champions Arsenal next Sunday.
Dyer said: "I've spoken to the chairman and my agent and it should be some time this week.
"It's a case of popping in after training and signing on the dotted line."
Dyer has had a turbulent time at St James' Park in recent seasons, falling out of favour with former manager Sir Bobby Robson, while the toon army faithful also turned on Dyer, however, he has once again regained their trust and respect despite the club having yet another disappointing season.
"It's a strange situation, in a way it was a blessing in disguise," he added.
"The whole episode, it was the kick up the backside I needed.
"It made me knuckle down and redeem myself and put in not just an occasional performance but performances week-in; week-out."
Dyer also believes those performances enabled him to win the fans over once again.
"That started to show towards the end of last season. I think the fans appreciated it, the majority have forgiven me. In a way, the start of last season was probably just what I needed," he said.
"At the start of last season, I knew my situation with how many years I had left.
"I honestly thought I would be seeing out this year and going somewhere on a free transfer. I didn't think for one instant I would be signing a new contract here, that's how bad it was.
"But people change, their opinions change. Mine has changed and I think the fans' has changed, so that's all good."