The Brazil midfielder will join the club on July 1, alongside Leipzig midfielder Naby Keita, following the conclusion of a medical on Monday and finalising terms on a long-term contract.
The deal has taken many by surprise, with initial reports of a deal only breaking on Monday via the French media, shortly confirmed by local club journalists.
“This is something that I always wanted – this is a giant of a team. The infrastructures of the club look exceptional.
“A football club of this size coming after my services, I didn’t have to think that much about coming over.
“I will try to create my own history at this football club. Hopefully, on a personal level, I’m able to win titles with this club.
“I will try to grow and learn and improve myself, and to be part of the club’s history.”
Fabinho, who has four caps for his country, is not in Brazil's World Cup squad for this summer's tournament in Russia. He is the club’s first signing of the summer transfer window, whilst Nabil Fekir is also expected to make the move.
The 24-year-old made 225 appearances for Monaco, where he started as a right-back, before becoming the more traditional defensive midfielder. He has scored 29 goals in five seasons in Ligue 1.
Fabinho is the ideal replacement for Emre Can, who is making the move to Juventus following the conclusion of his contract this summer. He is thought to be a versatile and physical presence in the centre of the park.