"PSG is delighted to announce that Marquinhos has signed a five-year contract with the club after transferring from AS Roma," the Qatari-owned French champions said in a statement.
Serie A side Roma said separately that the fee was 31.4 million euros (£27m), with €2.7m of that due to Sao Paulo club Corinthians.
The 19-year-old Marcos Aoas Correa, 'Marquinhos', joined Roma from Corinthians, where he made his professional debut, last year.
"I am delighted to be joining Paris Saint-Germain, a club where so many Brazilians have played and helped write the club's history," Marquinhos told the PSG website.
"I will do everything I can to continue that tradition and write my own name into the club's illustrious history books."
Uruguayan international Cavani, top scorer in Serie A last season, signed a five-year deal on Tuesday that media reported to be a French record 64 million euros.
PSG have spent more than 200 million euros on transfers over the past two years.
While Marquinhos left, Roma completed the signing of Dutch international midfielder Kevin Strootman from PSV Eindhoven on a five-year contract for a 16.5-million-euro fee and a further 3.5 million in potential bonus payments.
The 23-year-old joined PSV two years ago from FC Utrecht and has become a regular in the Dutch national team.
PSV technical manager Marcel Barends said on Tuesday that the offer had been one of the biggest fees in the Dutch club's history and "impossible to turn down".