The 25-year-old made his Spain debut against Serbia earlier this year.
Garcia joined Benfica from Spanish giants Real Madrid in 2009.
Garcia will replace Nigel de Jong, who left City for AC Milan earlier on Friday.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.