Rodwell made the switch from Manchester City to the Black Cats on Tuesday for around £10 million.
The 23-year-old's career has stalled since his move to the Etihad Stadium back in 2012, as he played just 16 league games for City in the past two seasons.
City's embarrassment of riches in midfield limited Rodwell's chances, and he was firmly behind the likes of Yaya Toure, Javi Garcia and Fernandinho last term as they claimed the Premier League title.
However, Neville, who saw first hand the emergence of Rodwell at Everton, believes that the versatile midfielder will play his way back into the England set-up if he stays clear of injuries at the Stadium of Light.
Good move for Jack Rodwell-time for him to play every week and show everyone his ability-if stays injury free will be back in England squad!— Philip Neville (@fizzer18) August 5, 2014
Rodwell, who played just five times for Manuel Pellegrini's team last season, stated his intentions to use the move to help fire himself back into the fold with the Three Lions.
The club's official website quotes him as saying: "Watching the World Cup left a little bit of a bitter taste in my mouth. I was supporting the team 100%, but I also wanted to be there so I think it's time I put that right.
"Without doubt the last couple of seasons I have not played nearly enough football as I have wanted to play. Regular football is the most important thing for me. This is a great place for me to be."