PSG said the 19-year-old, who had also been chased by Inter Milan, would join them in January on a four-and-a-half-year contract.
He is in Brazil's squad at the Olympic Games in London and has also played for his country's senior side.
"By signing a young talent of the quality of Lucas Rodrigues Moura Da Silva, Paris Saint-Germain is already preparing [for] the future," the French club said.
PSG did not disclose the transfer fee which has been widely reported by local media to be about 45 million euros.
Qatari-backed PSG had already spent more than 100 million euros on players in the close season in an attempt to dominate Ligue 1 and challenge for European honours.
New signings have included forward Zlatan Ibrahimovic and defender Thiago Silva from AC Milan and Argentine forward Ezequiel Lavezzi from Napoli.
Their splurge is bound to raise questions about whether they can fit in with UEFA's Financial Fair Play policy designed to stop clubs spending more than they can afford.
Lucas, an attacking midfielder, helped Brazil win the South American under-20 championship in Peru last year, scoring a hat-trick as they demolished Uruguay 6-0 in the final.
He made his Sao Paulo debut in 2010, having joined the club five years earlier.
