Talks had been ongoing between the pair over the last week since relegation from the Barclays Premier League followed their historic FA Cup win.
Martinez has been linked with the vacant job at Goodison Park ever since David Moyes was announced as Sir Alex Ferguson's successor at Manchester United and the Toffees made their move on Friday.
That appears to have persuaded the Wigan manager the time was right to end his four-year association with the club and although Whelan will not stand in the way of the 39-year-old, he will demand compensation.
Martinez remains in his post for the time being but Whelan told Press Association Sport: "Roberto wants to move on and I have got to accept it.
"Everton rang me and I said they have permission to talk to him. I would never stop Roberto talking to football clubs.
"We will let him go but he's on a 12-month rolling contract so if he moves someone will have to buy him out of his final year.
"We are still friends, we will always be good friends and he will always be a friend of Wigan Athletic."
- Sports & Recreation
- Sir Alex Ferguson
- Manchester United
- David Moyes