Martinez had become the favourite to succeed Gerard Houllier at Villa Park but has chosen to sign a new contract at the DW Stadium.
A Villa statement read: "Roberto met with his chairman earlier this week and he made the decision to honour his commitment to Wigan.
"The club would like to thank Wigan Athletic Football Club and its chairman, Dave Whelan, for their professionalism in dealing with our request to speak to Roberto Martinez.
"Roberto's qualities as a young and aspirational manager ensured him of a position high on our shortlist of potential new managers.
"Given that he had one year remaining on his contract at Wigan, we made an official approach through the proper channels, though we were aware of a commitment he had made to his club to agree and sign a new contract following the final game of last season.
"Roberto met with his chairman earlier this week and he has made the decision to honour his commitment to Wigan.
"Therefore, we have not met Roberto and we have not had the opportunity to discuss the vacant managerial role with him.
"We remain focused and are working hard to secure the best candidate for Aston Villa who will complement the club's commitment to be true to our heritage, competitiveness and passionate fanbase, and will have the new manager in place to prepare the players for the pre-season programme and next season's campaign."