Hibbert joined the Merseyside club in the year 2000 and since then he has played over 250 matches for The Toffees, and Neville paid tribute to the defender, hailing his loyalty to the side.
"If you stay at a club for 10 years and play in the first team for 10 years, a testimonial is just rewards," Neville told BBC Radio Merseyside.
"Loyalty is a massive thing and there are a lot of players in the team now that have been at the club a long time. Tony's been here 10 years and he's been a stalwart.
"You can't envisage him wearing another shirt. He's Everton through and through."
Hibbert’s testimonial will be against AEK Athens, the opposition in 2009 when he equalled the club record for most European appearances.
Neville added: "Somebody asked me the other day what he's like.
"I told them to come and see him in derby week. He just comes alive. From being a quite quiet lad, who does join in the with the banter but he's quite reserved, he comes alive.
"He leads from the front and he lets people know, particularly the foreign players, what it means to be an Everton player playing against Liverpool and what it means to the fans.
"In the squad we've got, he's probably the best out-and-out defender we've got.
"When people think of the great teams that have been built here over the last 10 years and some of the great performances, Tony Hibbert has always been in the starting XI.
"It's a tremendous achievement and I hope the fans come along and support him."
The game vs AEK Athens will be the last pre-season friendly at Goodison Park before they face Manchester United in the opening match of the 2012-13 Premier League season on August 18.