The Latics confirmed the Stamford Bridge club's fifth offer has met their valuation and they have given the forward permission to talk to Chelsea.
A statement on Wigan's official website read: "The club can confirm that after four unsuccessful bids from Chelsea for Victor Moses, a fifth bid has today finally met the valuation and terms set by Wigan Athletic and been accepted.
"The player has been given permission to speak with Chelsea."
Wigan's asking price for the 21-year-old was believed to be in the region of £9million.
The Nigeria international's displays toward the end of last season were key in keeping Wigan in the Barclays Premier League and he put in another impressive performance against Chelsea in the Blues' 2-0 victory at the DW Stadium on Sunday.
Latics boss Roberto Martinez claimed earlier on Thursday there had been no further developments in a potential move, but admitted he was the "wrong man" to ask.
But he revealed every one of his players had a price.
The Spaniard said: "You will get all sorts of speculation and talk, but the reality is every player has a valuation. If a club matches that valuation, then maybe you have to sit down with the player and there is a decision to be made."
On Moses, he said: "Victor is an incredible young man and I think the maturity he showed on Sunday is not normal in a 21-year-old.
"It has been a real joy to see him grow over the last few seasons. We made a massive investment in him as a young man and we are very proud of him."
Moses joined Wigan from Crystal Palace on a three-and-a-half-year deal midway through the 2009/10 season for a reported fee of £2.5m.
Should he complete a move to the Champions League winners, it would mean another exciting young attacker for boss Roberto Di Matteo to go with other summer acquisitions Eden Hazard and Oscar.
Martinez has already made four additions to his group this summer, recruiting defender Ivan Ramis, midfielder Fraser Fyvie and striker Arouna Kone on permanent deals from Real Mallorca, Aberdeen and Levante respectively, and Arsenal winger Ryo Miyaichi on a season-long loan.
And he revealed one more player could come in before the transfer window closes.
"At the moment, we are still looking at if we can bring in maybe another player, but it has to be the right one and he has to be the right character to fit in," Martinez said.