The 22-year-old said he would never play for Newcastle again after his name was mispronounced by team manager Joe Kinnear during a post-match television interview after the 2-1 defeat by Manchester City last Wednesday.
Wigan manager Steve Bruce said the move would be a boost for N'Zogbia after an unhappy spell in the northeast.
"We have agreed a fee with Newcastle and it's up to us now to convince the boy Wigan is the place to come and enjoy himself, kickstart his career...it seems to have gone a bit sour in the north-east," Sunday's British newspapers quoted Bruce as saying.
N'Zogbia, who joined Newcastle from French club Le Havre in 2004, has been linked with a move to several Premier League clubs in the transfer window.
The Times said on its website the club's had agreed a fee of six million pounds ($8.59 million) with Wigan defender Ryan Taylor moving to Newcastle as part of the deal.
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