The transfers in were offset by the departure of Dutch midfielder Nigel De Jong to AC Milan and Paraguayan striker Roque Santa Cruz's loan to Spanish side Malaga. City also brought in Matija Nastasic from Florence and Scott Sinclair from Swansea City. City's new signings will join up with their team-mates and manager after the international break.
Garcia, a 25-year-old product of Spanish champions Real Madrid's youth academy, was valued at £15.8m.
Meanwhile, Sinclair has expressed his delight at finally having joined City. The England winger played a key part in Swansea City's success last season and will be hoping to continue that good form at the Etihad.
"I'm just glad everything is settled and that I'm now a City player. There were times when I thought it might not happen so I'm relieved that I'm here and I can't wait to get started. Playing alongside some of the best players in the world is exciting for me and when you see two Champions League fixtures against Real Madrid on the horizon, it brings it all home," the former Chelsea player told the club's website.
Group of Death
City will need all of their considerable resources if they are to put on a better show in the Champions League this season than last. The English champions have been drawn in the proverbial "group of death", where they will face a trio of national and European champions - Germans Borussia Dortmund (Champions League winners 1996), Dutchmen Ajax (Champions League winners 1971, 1972, 1973 and 1995) and Spanish powerhouse Real Madrid, who have won the Champions League a stunning nine times.
City were eliminated in the group stages last season, having been matched with Napoli, Villarreal and eventual finalists Bayern Munich.