The striker was found guilty of sexual assault and actual bodily harm over an incident in a London nightclub, which occurred in December while he was on loan at Hull.
King spent a subsequent spell on loan at Middlesbrough before returning to the Latics in the summer but he will now be left without a club after a mandatory notice period has expired.
Whelan told Sky Sports News: "We have to follow the rules and regulations which means we will have to give him 40 days notice that his contract will be cancelled.
"He is absolutely sacked - we will not tolerate football players who get sent to jail for 18 months. As far as we are concerned, he is finished with football at Wigan Athletic."