Moyes managed Neville during part of his 11 years in charge at Everton, during which he regularly challenged for European football and claimed a fourth-place finish in 2004/05.
His impressive work earned spells at Manchester United and Real Sociedad, and Neville said: "David Moyes being back in the Premier League is fantastic.
“He's picked a club that needs somebody like David Moyes. He'll bring a lot of stability at Sunderland. He'll try to bring through the academy players and unearth a gem."
Neville - who made 505 Premier League appearances at Man Utd and Everton before becoming a part of Moyes' coaching staff at Old Trafford - expects an emotional evening for his old manager at the Stadium of Light on Monday.
"He will have a lot of emotions playing against Everton," Neville added. "They gave him his shot in the Premier League so Moyes owes Everton a great deal, but Everton also owe him a great deal. I hope he gets a great ovation."