Martinez guided the club to a remarkable FA Cup triumph this season but was unable to prevent his side from suffering relegation to the Championship, as they finished in 18th place in the Premier League in the last year of the Spaniard's four-year reign.
Wigan chairman Dave Whelan said, "He wanted permission to move so I've given that. He has 12 months left on his contract, so whoever comes in for him must pay the remainder of his contract.
"He feels he's not the man to lead us back into the Premier League. I've got to accept what he feels. He loves Wigan and the fans. We have to move on now and want applications for the job."
Martinez, who once played for the Latics, joined as manager in 2009 after leaving Swansea City and had kept the club in the Premier League since then until this season. Yet despite beating Manchester City 1-0 at Wembley to win the FA Cup, Martinez proved unable to keep Wigan in the Premier League. Despite that, the Spaniard has received much praise for working within tight financial constraints and playing an attractive brand of football.