The player from Rio de Janeiro won both the Copa Libertadores and Copa do Brasil with Flamengo last year but will now be moving to Palace for an undisclosed fee.
He follows Jefferson Lerma as a pre-season arrival at Selhurst Park, with Palace chairman Steve Parish telling the club's website: "Matheus is a young and exciting player whose impressive early progress we have followed with keen interest, and we are delighted to welcome him to the club.
"Palace have a long history of attacking players with skill, pace, and tenacity, and I am sure Matheus will be another popular addition to the nucleus of this young and entertaining squad, packed full of international talent and potential, that we are building here in south London."
Franca added: "I'm very happy to be here. I hope I can bring good results for our supporters, for the other players and everybody else in the team."
