The 19-year-old Brazilian has signed a contract from January 2013 to July 2017 for a fee believed to be in the region of €43m (£33m).
"Paris Saint-Germain and Sao Paulo FC have reached today an agreement for the definitive transfer of Lucas Rodriguez Moura Da Silva," read a statement on PSG's official website.
"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."
Moura, who is currently on Olympic duty with the Brazilian national team, had been heavily linked with a move to Manchester United.