Talks had been ongoing between the pair over the last week since relegation from the Premier League followed their historic FA Cup win.
Martinez has been linked with 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."
Whelan said the club's relegation had been the main factor in Martinez's decision to seek a new challenge.
"He does not feel he is up to the task of getting us back into the Premier League," added the Wigan chairman. Whelan had hoped to hang to Martinez after the pair met on Thursday and the Spaniard had made certain requests about improving the club's training ground and youth development.
That appeared to put the ball in the chairman's court but having had the weekend to think about things Martinez decided he could not continue.
"It is remarkable what he has done for Wigan," added Whelan.
"He kept us in the Premier League up to this season and won the FA Cup - what more could he do?
"We have had great success together and we will always be friends for life - I have great respect for him."
Crystal Palace are likely to try to loan back flying winger Wilfried Zaha from Manchester United next season after securing promotion to the Premier League.
The south Londoners beat Watford 1-0 in the Championship play-off final on Monday.
The 20-year-old Zaha won the spot kick that sealed victory in what was meant to be his final Palace game before joining champions United.
"They might want him to get experience in the Premier League playing for us rather than maybe not playing for them. I don't know, of course," Palace co-chairman Martin Long was quoted as saying by www.skysports.com on Tuesday.
"We probably will ask."