The Toffees skipper has heaped praise upon the Republic of Ireland international and states that big things are expected of the central midfielder
David Moyes signed 24-year-old Gibson from Manchester United for an undisclosed fee believed to be in the region of £500,000 and Neville believes that it was a bargain buy.
"Darron has been a revelation to play with since he arrived," Neville told BBC Sport.
He added: "It has to be one of the snips of the century as it was well under £1million to get someone of his quality and grounding.
"There is always that doubt when someone comes from a top side like Manchester United and they are not a consistent member of that team, playing every other two to three weeks.
"You wonder why; is it fitness, is it something else? I've been in that situation and the bottom line is in front of Darron he had Michael Carrick and Paul Scholes, two of the best central midfielders in the Premier League - that was the challenge.
"When you are playing in Manchester United reserves there are always question marks against you but since he has come to Everton he has answered a lot of those questions.
"We expect massive things from Darron at this club," continued Neville. "He doesn't realise how good he can be.
"We have someone in midfield with energy, quality and more importantly the hunger to play at the highest level and that is driving everyone forward," he added.
"He has quality on the ball and his set-piece delivery is fantastic and to me he looks like someone who could be a five to 10 goals a season man."