Portugal midfielder Matheus Nunes in action for Wolves against Manchester United. AFP
The Premier League champions had a previous bid for Nunes rejected, with the 25-year-old subsequently choosing not to train with Wolves in a bid to force through a move in the final days of the transfer window.
Speaking earlier this week, O'Neil said he was unaware of any improved bid from City and expected the player to remain at the club beyond Friday's transfer deadline.
But the clubs have come to an agreement which involved a bigger fee.
"The situation is resolved, he is signing for Manchester City," said O'Neil. "If he had re-joined the group I would have told him what I felt.
"When I dealt with him before, he worked hard and did what he could for the club. Then a big club came calling and players want to play for Manchester City. We move on."
O'Neil was asked what had changed with the Nunes deal.
"The offer," he said. "At that point it was a lot lower and we weren't going to accept. The squad will be in a better place than it was last week by the end of the window."
Nunes became Wolves' then record signing when he joined from Sporting Lisbon for an initial £38 million last year.
He made 34 top-flight appearances last season, scoring one goal.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)