A World Cup winner with Argentina, the 23-year-old forward has scored 10 goals in 33 appearances since moving from River Plate last summer.
Alvarez initially joined on a five-and-a-half-year deal but has now signed an "improved" contract reflecting his performances for club and country.
He said City offers him "everything he needs" to reach his best.
"For a club like City to put their faith in me like this is amazing," Alvarez said.
Alvarez initially joined on a five-and-a-half-year deal but has now signed an "improved" contract reflecting his performances for club and country.
He said City offers him "everything he needs" to reach his best.
"For a club like City to put their faith in me like this is amazing," Alvarez said.