The LA Galaxy midfielder played with the former Manchester United full-back for over a decade during a trophy-laden spell at Old Trafford.
And Beckham, who is currently in Greece as part of the London 2012 delegation bringing the Olympic torch to the UK, believes appointing the 37-year-old is a wise move by the new manager.
“I think it's great. Gary has knowledge throughout the game,” Beckham told reporters.
“He's been in big tournaments [and] he's played for England for many years.
“Gary has always been very vocal about many things. He's had the experience of being through tournaments and being disappointed in tournaments and knowing what he thinks have been the problems - that's why it's a clever move and great for the team.
|Parker doubt for Euros
“Let's hope we go out there and we're successful. It's a new team, young players.
“It's one of the first times we have gone into a big competition without huge, huge expectation on our shoulders - that could maybe be a good thing for the team.”
The US-based midfielder also hopes Neville can inspire his former England team-mates and the younger generation of players alike to major tournament success for the first time in 46 years.
“[Neville's appointment] is a very clever thing but it's also great for the players and the manager,” Beckham continued.
“To have someone with his knowledge as well as Roy's knowledge - it's a very clever thing to do. I wish Gary the best of luck.
“I hope we can go all the way - that has obviously always been our main objective in every competition that we have gone in to. You do not go in to a competition thinking 'let's see if we can make the quarters and see what happens'.
“You always go in thinking you can go all the way. Whether it happens - which obviously it has not happened in the last quite few years - that always remains the objective.”