The 19-year-old Brazilian has signed a five-year contract at Selhurst Park.
Franca's arrival will augment a Crystal Palace attack that was robbed of the services of long-term talisman Wilfried Zaha earlier this summer when he chose to join Galatasaray in Turkey at the end of his contract.
Franca scored nine goals in 54 appearances for Flamengo after breaking into the first team in 2021.
"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," Franca told cpfc.co.uk.
"I'm very excited for my first game here at my new home, giving my best for my new team. I hope all the supporters are happy with me coming here. I bet it is going to be good for all of us."
Chairman Steve Parish added: "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."
Palace signed Jefferson Lerma on a free transfer from Bournemouth earlier this summer.
They begin their Premier League campaign away at Sheffield United next weekend.
