The Argentine goalkeeper has put pen to paper on a long term extension to 2029 at Villa Park.
Martinez, who won another Copa America this summer, was expected to leave for a top club.
On why he stayed, he told club media: “I feel that the club is moving forward every year. I have achieved everything as an international for Argentina and I still think that we can win a trophy here. I will have a go in the next five years and see if we can achieve that.
“I became the best in the world here and I want to continue developing myself. I’ve got an amazing goalie coach and an amazing manager.
“This club wants to progress. Defending the goal at Villa Park is exciting and I get goosebumps every time I hear my name in the stadium.
“I feel the same love here as I feel for the national team, so why change?”