Manchester City, Benfica and Real Betis all wanted Oubina, 25, who signed for Brum on a season-long loan with a view to a permanent £6million deal next summer.
Oubina, who has won two Spain caps, has agreed a £25,000-a-week deal with the Blues which will quadruple his current earnings at Celta who were relegated last season.
Oubina wanted a permanent deal, but Celta would only agree to a loan so they stand a chance of getting him back next summer if they return to the Primera Liga.
Oubina said: "I'm happy. I'm going to play in such a powerful and attractive league.
"I would have liked Celta to transfer me and not go out on loan but the club didn't want that."