Both companies compete in Mexico with America Movil, the company controlled by billionaire Carlos Slim, which has long dominated the telephone market in Latin America's no. 2 economy.
Aya said the agreement was part of a trend that was taking place globally to better position companies against rivals.
"You need a lot of scale to compete in this business," Aya told reporters at an event in Mexico City.
Miguel Calderon, vice president of regulation at Telefonica Mexico, said the deal would ensure the firm remained in Mexico.
The company was open to working with the Mexican government on its telecom projects, Calderon added.