The 16-year-old, from Nantwich, has decided against signing scholarship forms at Gresty Road in favour of a switch to Stamford Bridge.
Crewe are expected to receive a fee in the region of £300,000 plus add-ons for the tall schoolboy, who had been linked with a number of Premier League clubs including Spurs.
Manager David Artell said he was unaware of the situation on Monday afternoon.
He said: "I assure you, I don't know. I wasn't in the academy meeting this morning, but if that's the case then good luck to him, I wish him all the best. I hope it works out for him.
"George, I'm fairly confident, would have played in our first team but there's no guarantee. If he's decided to move then good luck to him.
"That's what Chelsea do, it's their business plan. Good luck to them."
Nunn, who has changed his Facebook profile to say 'Striker at Chelsea Football Club', had long been earmarked as an academy player with true star potential.
Head of coaching James Collins, meanwhile, told the Crewe Chronicle: “I spoke to [Nunn] and his parents. In my opinion he could have been around our first team in 12 month's time, but now he'll have a challenge just to get in Chelsea's youth team. I feel being around a first team is a better experience.
“But there are no hard feelings and we all wish him well for the future.
“We think our product speaks for itself. Seeing our young players leave early is not what we plan for, but there's no panic. There are others in that age group with equal potential, and it'll be interesting to see where they all end up."
Nunn's exit is similar to that of Daniel Trickett-Smith, who joined Liverpool as a 16-year-old in 2012 for a similar fee, but now plays for Leek Town.