The 19-year-old has long been linked with a move to Europe, with Manchester United and Inter Milan the long-term front-runners for his signature.
However, the player admitted earlier this week that he was in advanced talks with Les Parisiens, and the the Ligue 1 outfit confirmed on Wednesday that a transfer had been agreed.
A statement on the club’s official website read: “Paris Saint-Germain and Sao Paulo FC have reached today an agreement for the definitive transfer of Lucas Rodriguez Moura Da Silva.
“The player and Paris Saint-Germain have also signed an agreement from January 2013 to July 2017. The player will join Paris Saint-Germain and his new teammates in January 2013 for the second half of the season 2012/2013.
“By signing a young talent of the quality of Lucas Rodriguez Moura Da Silva, Paris Saint-Germain is already preparing the future.”
Lucas becomes Carlo Ancelotti's fourth major signing this summer, following the arrivals of countryman Thiago Silva, striker Zlatan Ibrahimovic and Argentina international Ezequiel Lavezzi.
He is believed to have signed a contract worth250,000 euros a month, putting him on a par with some of the club's top earners.
Lucas is currently on international duty at the Olympic Games, as Brazil's U-23 squad attempts to win gold for the first time when it takes on Mexico on Saturday.