The 19-year-old, who spent last season on loan at Real Madrid, becomes Monaco's 10th summer signing following in the footsteps of illustrious names such as Radamel Falcao, Joao Moutinho, James Rodriguez and Eric Abidal.
A statement on Monaco's club website said: "Monaco are pleased to announce the arrival in the professional team of Fabio Henrique Tavares, also known as Fabinho, a Brazilian right-back of 19 years who has had spells with Fluminense and Real Madrid.
"Fabinho is loaned for one season by the Portuguese club Rio Ave."
The Brazilian full-back made just one first team appearance last season for los Blancos, getting an assist in his 15-minute cameo in Madrid's 6-2 win over Malaga.
Elsewhere, the Ligue 1 new-boys are set to complete the permanent signing of Siena goalkeeper Gianluca Pegolo.
The Italian club's sporting director Stefano Antonelli told Sport Italia: "The transfer talks are close to completion. I think it will be done by the end of the week."
Pegolo, 32, is about to enter the final year of his contract, and will be allowed to leave after Siena suffered relegation from Serie A last season.