Barca and La Real have been negotiating for Bravo since the end of last season and a deal was delayed due to Barca midfielder Jonathan dos Santos' resistance to join the Basques on a permanent basis as part of the deal.
The two clubs eventually reached a deal, believed to be worth around 12million euros (£9.6 million).
Bravo has agreed a four-year Barca contract.
He is the second goalkeeper to join Barcelona this summer, with 22-year-old Marc-Andre Ter Stegen signing from Borussia Monchengladbach last month.
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