The Universal film is in the writing stage right now.
It will be directed by "Whiplash" helmer Damien Chazelle from a script by "Spotlight" scribe Josh Singer, reported Deadline.
Chazelle and Gosling, 35, are currently together making "La La Land", the musical film set in contemporary Los Angeles.
"First Man" is based on James Hansen's biography "First Man: A Life Of Neil A Armstrong" and the astronaut's historical 1969 mission on Apollo 11 is approaching its 50-year anniversary.
Chazelle boarded the film in the spring after it had originated at Warner Bros with Clint Eastwood planning to direct in produce. Temple Hill partners Wyck Godfrey and Marty Bowen are producing now.