Fernando Torres is to return to Atletico Madrid on loan until the end of the 2015-16 season.
Steve Clarke is hoping to keep Glenn Murray at Reading after his loan deal expired following the 2-1 win over Norwich.
The former Halifax boss, who had been at the helm since December 2008, led his side to a 1-0 win over Torquay at the Kassam Stadium on Saturday afternoon before the U's chairman Ian Lenagan broke the news.
"My understanding is that Chris has told the players he has resigned," he said.
"And he told me yesterday that he would be resigning at the end of this match."
Wilder, who took Oxford out of the Conference and back into the Football League three years ago, was the third longest-serving manager in the country and left with United sixth in League Two.
There has been strong speculation in recent days linking Wilder to the vacant manager's position at League 2's bottom club Northampton.