Previous coach Diego Alonso left after taking charge for the team's inaugural season; they finished 10th in the Eastern Conference before losing to Nashville in the play-in round of the playoffs.
As well as bringing in Neville, Inter Miami have also announced Chris Henderson as their new chief soccer officer and sporting director.
"I am incredibly delighted for this opportunity to coach Inter Miami and to work with Chris and the entire ownership group," said Neville, who can start his new job once he receives a work visa.
"This is a very young club with a lot of promise and upside, and I am committed to challenging myself, my players and everyone around me to grow and build a competitive soccer culture we can all be proud of.
"This fantastic soccer-loving market deserves consistent performances and a winning mentality, and I look forward to getting to work."
The Football Association (FA) confirmed earlier on Monday that Neville had stood down from his England post with immediate effect.
Co-owner Beckham believes Neville's experiences as both a player and a coach can help Inter Miami to success on the field, describing his long-time friend as a "natural leader".
"I have known Phil since we were both teenagers at the Manchester United academy. We share a footballing DNA having been trained by some of the best leaders in the game, and it's those values that I have always wanted running through our club," he said in a statement.
"Phil has deep experience in football, as a player and as a coach at both club and international level, and over his career he has worked with many of the finest managers and players in the game.
"I know his qualities as a person, his decency, loyalty and honesty - and his incredible energy and work ethic. Anyone who has played or worked with Phil knows he is a natural leader, and I believe now is the right time for him to join."