The Rio de Janeiro club did not reveal details of the fee they will receive for the 21-year old, but said it was close to his buy-out clause and "a very good deal for Flamengo in terms of values."
Brazilian media reports said the fee was 35 million euros ($40 million).
Attacking midfielder Paqueta, who has been compared to AC Milan's most famous Brazilian Kaka, made his debut for Flamengo in May last year and has played 58 times for the first team. He was capped by Brazil for the first time last month.
He will remain in Brazil until the end of the season in December.
Flamengo are challenging for the Serie A title and currently sit third in the table with nine games remaining.
($1 = 0.8684 euros)
(Reporting by Andrew Downie; Editing by Toby Davis)
