Moses played well against Roberto di Matteo's men last weekend and the Londoners came back with their fifth offer - believed to be in the region of ?9million - which the club have reluctantly accepted.
A statement from Wigan said: "The club can confirm that after four unsuccessful bids from Chelsea for Victor Moses, a fifth bid has finally met the valuation and terms set by Wigan Athletic and been accepted."
It added: "The player has been given permission to speak with Chelsea."
To make matters worse for Roberto Martinez's side, they will travel to face a Southampton side in buoyant mood ahead of their first home game back in the big-time after their narrow opening defeat at Manchester City.
Saints boss Nigel Adkins said: "Obviously scoring a couple of goals away from home has given the players a bit more belief.
"They have trained very hard this week. The lads that played had an MOT and recovery session and the lads that didn't had a training session and were bang at it. There has been a buzz about the training ground this week."
Source: PA
Source: PA