The 24-year-old joins Liverpool on July 1, having made 225 appearances for Monaco and winning the Ligue 1 title in 2016-17.
Liverpool confirmed the deal on Monday evening, with the signing coming as a surprise to many with reports leaking just hours before.
“He is tactically very strong and football smart. I think he improves our squad and there aren’t that many players you can say that about in this moment, because the quality we have already is so high.
“I like that he is young yet experienced also, with a high number of games at a club that compete to win. Also, international caps for Brazil tells you something about him.
“This signing gives us new opportunities and for that I am excited. I’m sure our supporters will make him very welcome and at home at our wonderful club and in our amazing city.”