Paramount had planned to produce Beverly Hills Cop 4, but the studio dropped the project in 2016 and has now sold the rights to the streaming giant.
Murphy first played Foley in 1984 and played him again in 1987 and 1994.
The 58-year-old received rave reviews this year for his role in the Netflix film Dolemite Is My Name.
The original Beverly Hills Cop saw maverick Detroit detective Foley travel to Los Angeles to investigate a friend's murder.
Harold Faltermeyer's theme for the film was a top 10 hit in 1985 and became a hit again 20 years later when it was covered by Crazy Frog.
Jerry Bruckheimer, who produced the first two films, will also be in charge of the new project, according to the Hollywood Reporter.