The 24-year-old escaped punishment from the Football Association, despite lunging into Luiz with a two-footed tackle during City's 2-1 victory over Chelsea in the FA Cup semi-final on Sunday.
Following the FA's verdict, Aguero issued an apology via his Twitter account to the Brazilian claiming that it was an "impulse reaction".
Luiz responded on the social networking website saying: "Thank you Sergio Aguero for a demonstration of character. We get to know great man and athletes this way."
The English governing body stated that they did not take retrospective action against the incident because match referee Chris Foy made a decision regarding the tackle when he saw part of it during the game.