The 20-year-old had been training with The Cobblers, and Kevin Wilson offered him the opportunity to sign with the Division Two side, only for The Magpies to make their swoop.
"He really is a very highly-rated young player," said executive deputy chairman Peter Storrie. "We are very pleased to have signed him.
"Northampton offered him a contract, after we showed an interest, but I think it was too late.
"With no disrespect to Northampton, I think he realised it would be a step up for him."
Nicholson had been with Town on a non-contract basis, but he has now put pen-to-paper on a three-year deal at Meadow Lane.
Meanwhile, Northampton have persuaded experienced defender John Frain (pictured) to sign a new two-year contract.
"I am delighted John has signed this new contract," commented manager Kevin Wilson.
