The Colombian worldwide will undoubtedly strengthen Barcelona's defensive side, especially with Javier Mascherano expected to leave the club.
According to Barcelona's official website, Mina cost €11.8 million (£10.5 million).
Mina, 23, moves to the Camp Nou for a fee of €11.8 million, and the Colombian's five-and-a-half-year contract includes a €100m release clause. He will bring a physical presence as his 1.95 metre frame suggests but he is also a quick, ball-playing defender.More news: Longhorns shooting guard Andrew Jones diagnosed with leukemia
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He will be Barcelona's second signing of the January transfer window after Philippe Coutinho's 160 million-euro capture from English topflight, Liverpool.
The center-back has proved himself a strong asset to his former team, supporting them to triumph as league title-winner in 2016 and scoring a total of nine goals during the team's 49 matches.
Mina was a key part for Palmeiras when it won the Brazilian league in 2016 and was runner-up previous year.
The table-toppers said in a statement: "Yerry Mina now comes to Barca with the opportunity to continue developing as a footballer following his move to Europe".