Reports emerged earlier this evening claiming that the Reds were close to sealing their first signing of the summer, and the club have now confirmed that the 24-year-old midfielder will officially complete his move on July 1.
The fee taking Fabinho to Anfield has not been disclosed, but it is understood to be worth up to €50m (£43.7m).
"I am really excited about this move. This is something that I always wanted – this is a giant of a team. The infrastructures of the club look exceptional," the Brazil international told the club's official website.
"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 leaves Monaco after making 225 appearances and scoring 29 goals for the club over his five-year stay, is likely to be a direct replacement for Emre Can, who is expected to leave the club when his contract expires this summer.