Valencia, who qualified for the Champions League group stage on Tuesday when they won their playoff against Monaco, needed to bolster their defence after they sold Argentina centre back Nicolas Otamendi to Manchester City last week.
"I am happy and honoured to sign for a great European club," Santos said on Valencia's website.
"Playing in the Champions League and La Liga are important goals for me," added the 26-year-old, who has a market value of 7.5 million euros (5.48 million pounds) according to website Transfermarkt.com.
Neither Valencia or Braga revealed the financial terms of the deal.
Valencia, who were Champions League finalists in 2000 and 2001 and were taken over last year by Singapore billionaire Peter Lim, were drawn in Group H of Europe's elite club competition earlier on Thursday with Zenit St Petersburg, Olympique Lyonnais and Ghent.
(Reporting by Iain Rogers, editing by Pritha Sarkar)
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