The 19-year-old will remain with the Brazilian side until the new year before linking up with Carlo Ancelotti's side on a four-and-a-half-year deal.
The playmaker, who is currently in Britain representing Brazil at the Olympics, began his professional career with his hometown club and has made 58 league appearances.
Moura, had been a target of Manchester United, but the two clubs failed to agree on a fee for the teenager.
A statement on the PSG website said: "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."
