The 19-year-old will remain with the Brazilian side until January before linking up with Carlo Ancelotti's side on a four-and-a-half-year deal.
Moura, had been a target of Manchester United, but the two clubs failed to agree on a fee for the teenager.
"The player and Paris St Germain have signed a contract from January 2013 to June 2017. Lucas will join Paris St Germain and his new team-mates in January 2013 for the second half of the 2012-13 season.
"In signing a young player of the quality of Lucas Rodriguez Moura Da Silva, Paris St Germain are also building for the future."