Ajax will pay City 14 million euros ($15.32 million) for the 19-year-old winger.
Borges joined City's youth academy in 2014 from Sporting Lisbon and played for their Under-21 team last season, helping them win the championship in Premier League 2.
Ajax sign Portuguese winger Borges from Man City for £17m on long-term deal
Ajax Amsterdam have signed Portuguese youngster Carlos Borges from English champions Manchester City on a five-year deal, the Dutch club said on Thursday.