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 start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?