The 22-year-old Spanish international passed his medical on Friday as Monaco and Barcelona agreed to a season-long loan deal with an 11-million-euro fee ($12.9 million) to make the move permanent.
According to the same source, the contract will not be made official until the 1st of July.
Fati burst onto the scene at Barcelona aged 17, but has since failed to live up to initial high expectations.
He made 11 appearances in all competitions for the La Liga champions last term, without finding the net.
Fati spent the 2023/24 season on loan at Premier League club Brighton, where he scored four goals in 27 outings.
With his expected arrival, Fati should become Monaco's third signing of the summer. Former Manchester United midfielder Paul Pogba is slated to sign for the Ligue 1 side, following on from England international Eric Dier.
Pogba was also undergoing a medical with the principality side on Friday.
The 32-year-old 2018 World Cup winner is seeking a club after having his contract terminated by Juventus in March while serving an 18-month suspension for doping.
The trio should be officially announced to the press on the 3rd of July.
