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City's striker and Spain's World Cup winner won the prizes at a ceremony in Monaco.
After an opening half-hour in which the home side dominated possession, Alvarez broke the deadlock in the 31st minute.
Gvardiol is Pep Guardiola's second signing in this transfer window after Croatia midfielder Mateo Kovacic joined from Chelsea.
The Premier League heavyweights will visit India between September 21 and 27.
The 32-year-old has a contract until June 2025 with an option for a further year, while the Spanish champions also said they had included a buyout clause of 400 million euros ($435.72 million).
Gundogan will leave City after captaining the English club to the Premier League, FA Cup and Champions League last season, ending a successful seven-year stint in England where he won 14 trophies, including five league titles.
City were crowned European champions for the first time and they also secured the treble of Premier League, FA Cup and Champions League, with Guardiola becoming the first men's manager in history to achieve the feat on more than one occasion.
Puyol played alongside Guardiola for Barcelona and was captain of the Barca team managed by him a few years later, winning the Champions League in 2008-09 and 2010-11.
Chelsea sportingly gave the City players, who had watched the Arsenal game together the previous evening, a guard of honour before kickoff while thousands of fans rushed onto the field after the final whistle.
Pep Guardiola's City crushed United 6-3 in the Premier League on Sunday.