Since joining City from Atletico Madrid in 2011, the 30-year-old Argentine has helped the club win three Premier League titles and three League Cups.
Aguero is City's all-time record scorer with 204 goals, including the stoppage-time victor against Queens Park Rangers in 2012 that won a first top division title in 44 years.
Aguero has been linked with moves away from the Etihad since the arrival of Pep Guardiola but finished last season with more than 20 Premier League goals for a fourth successive campaign.
"The players are human and have families, but reason I'm always here is the new challenges".
Aguero was on £250,000-a-week, but the new deal is understood to put him alongside Kevin De Brune, as City's highest-paid players on around £350,000-a-week.
The City boss was banned from the touchline for the game and watched from the stands as his side conceded two first half goals before Bernardo Silva pulled a goal back in an improved second half.
"I am happy for this additional year", Agüero, City's all-time leading goalscorer, said. I'm very happy because they have treated me very well since the first day I got here.
"He has a problem in the bone of his feet, I don't know (when he will be back)", said Guardiola.
"I speak with the doctor sometimes, and he's telling me he's going so well. If you are not able to do it, then learn and improve".
"Before there were possibilities, but I believe that we are already at an age when each one is going to finish his career at the club he is in".