According to media reports Qatari-backed PSG paid a fee of 45 million euros ($59.3 million) for the exciting prospect in August, with an agreement that he would arrive in January.
The five-year deal was completed on Tuesday after Lucas, who helped his former club Sao Paulo to clinch the Copa Sudamericana last month, joined the Ligue 1 leaders at their training camp in Qatar.
“For sure all Brazilians talk about this dream and it was also my dream, and it’s an important step in my career because in Europe you play against the best players in the world in the best leagues in the world,” he told reporters.
“I think I have all the ingredients to succeed and to fight and I will train daily in order to reach this world level;” added Lucas who has won 22 caps for his country and has likened his style to that of World Player of the Year Lionel Messi of Argentina.
PSG have a tradition of signing top-quality Brazilians, especially in the 1990s when playmaker Rai and center back Ricardo helped them clinch their last French title in 1994.
PSG sports director Leonardo also spent a year as a player at the club before moving to AC Milan in 1997.