The 22-year-old has signed a five-year contract after joining the club for an undisclosed fee.
"I have joined a great team who had a great season last year to qualify for the Europa League, it is a dream for me," Garcia said.
"I prefer to play as a full-back, in the same position as Federico Balzaretti, but he is an important player so I will do my best to carve out my own place."
Palermo are rebuilding this summer as, despite a fifth-placed Serie A finish, they have lost defender Simon Kjaer to Wolfsburg, midfielder Mark Bresciano to Lazio and are set to sell striker Edinson Cavani to Napoli.
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