After resigning at the U’s on Sunday, the 46-year-old was unveiled as Cobblers manager yesterday morning.
With the club six points from safety in Sky Bet League Two, the race is on to make signings before the transfer window closes on Friday.
There was immediate concern among some U’s fans that Wilder could head back to tempt players and coaching staff away from the Kassam Stadium.
It is not clear whether a commitment not to return was part of the compensation package agreed between the two clubs, but Wilder has made it clear no attempt will be made.
“I get on with players, I have a relationship with them, but I won’t be going back there,” he said. “I don’t think that’s right and proper and fair.
“We will look around the market and I should imagine they won’t want to get rid of anybody just yet anyway with having a tight squad and going well at the moment.”
The same goes for staff, with Wilder naming Alan Knill as his assistant.
He said: “I’ve got no great desire to come and bring my own staff in straight away.
“I worked with staff at Oxford United, I came in on my own. I was prepared to look and to see.”
There was widespread confusion on Saturday night, when Wilder’s agent put out a statement saying he had not resigned within hours of U’s chairman Ian Lenagan claiming he had left the club.
The ex-Halifax boss defended his actions and is confident the move will prove to be the correct one.
“It was moving at a pace and I was told both clubs were talking and obviously wanted to get it over the line,” he said.
“I did my job professionally on Saturday. I think I’ve left the club in a fantastic position in terms of the league position and the assets on the pitch all tied up.
“It’s a good group of players who I expect to kick on into the second part of the season.”
He added: “Sometimes you have to make decisions, I’ve taken a brave one, but I feel it’s a correct one and I’m 100 per cent sure that I’ve made the right decision.”
Northampton chairman David Cardoza was thrilled with the switch.
He said: “The fact that we’ve got him from Oxford, who are a couple of points off second place to come down to a club that’s 24th is a huge coup for us.”