Bravo heads to West Yorkshire with an impressive cv, having served as Real Madrid's director of strategy from 2003 to 2010.
Since then, Bravo has worked as the director general of the Aspire Academy for Sports Excellent in Qatar.
"Leeds United is a club steeped in prestige with an extremely proud fanbase and I am thrilled to join the board of directors," he said.
"I hope my experience gained across the game will add value for the club and I look forward to working with the ownership, management and the whole team to take Leeds United forward, on and off the pitch."
The appointment is the first significant one made by co-owner Andrea Radrizzani since he bought a 50% stake of the club from Massimo Cellino in January.
"On behalf of everybody at Leeds United I would like to welcome Ivan to the club," he said. "He brings to the role a wealth of knowledge and expertise gained from leading roles at the very highest levels of the game.
"I look forward to working closely with Ivan as the club comes together to build on the progress achieved this season."