Chelsea have pursued Nigeria international Moses, 21, throughout the summer but the two clubs had been unable to agree a fee.
On Thursday night, though, Wigan confirmed that they have finally come to an agreement over his sale.
A Wigan statement 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."
Moses, who joined Wigan from Crystal Palace in the January 2010 transfer window, has entered the final year of his contract with the Latics but his club had been adamant that they would not sell at a price that did not suit them.
Earlier on Thursday, manager Roberto Martinez had warned that if Chelsea did not pay Wigan's asking price, believed to be in the region of £9 million, Moses would remain at the DW Stadium.
"You will get all sorts of speculation and talk, but the reality is, every player has a valuation," Martinez had said. "If a club matches that valuation then maybe you have to sit down with the player and there is a decision to be made.
"Here, for all the talk and speculation, we have never had an offer which matches what the club wants - so at that point, all the rest is cheap talk. 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. If there is nothing to consider, it is not an issue.''