The match, in Baltimore on July 31, pits manager Roberto Mancini against his former club and City's football administrator Brian Marwood said it was a fitting conclusion to the trip.
"It is a coup to be playing the team we hope will soon be Champions League winners and I think this is the type of fixture everyone connected with the club and our supporters in particular will relish," he told the club's website.
"I know Roberto's eyes lit up when we mentioned we were hoping to play Inter.
"Hopefully, this is just the beginning of playing this calibre of opposition on a regular basis."
City will also face Sporting Lisbon, New York Red Bulls and Mexico's Club America while in the USA.