The news comes after weeks of speculation over his future as Wigan failed to keep their place in the Premier League next year and were demoted to the Championship.
Confirming the news, Wigan owner Dave Whelan said, per BBC Sport:
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.
Roberto Martinez joined Wigan from Swansea in 2009, having previously played 229 times in his career for the team from 1995 to 2001.
The 39-year-old had previously coached Swansea from 2007 to 2009 and has been credited as the originator of their sleek passing game, which he also introduced at Wigan Athletic.
He recently won the FA Cup in unlikely fashion against Manchester City, then coached by Roberto Mancini. His only other title as manager is the Football League One trophy he won with Swansea.
Martinez has been linked with the vacant Everton manager post and his departure makes the move even more feasible.
A former Wigan Athletic teammate of Martinez, Dutch defender Arjan de Zeeuw, recently claimed that Martinez would leave Wigan if there was Premier League interest in him. Speaking to BBC, he said: "If there is interest from another Premier League club, I think Roberto will leave Wigan. [If I were Everton's chairman] I would definitely be asking the question and give him a phone call and see what his thoughts are."