O’Connell has nailed down the role as the left-sided centre-half in Wilder’s defence over the last couple of season.
But the Blades boss insists Robinson, who completed his move from Nottingham Forest, hasn’t been signed just to provide cover at the back.
Wilder said: “I have no cover positions at all, I've got a really good group of 21-22 players. No one is cemented in and no one is on the outside forever.
“Jack O'Connell has been a big favourite here but I think he recognises now he needs gentuine competition and Jack (Robinson) will prove that. I'm betting he will push hard and give Jack O'Connell a problem and that's something we should embrace as a football club.”
Wilder is delighted to have finally got his man, having tried to sign Robinson a couple of years ago while he was at QPR.
And he revealed the 26-year-old’s attitude and grounding at Liverpool, where came through the academy, were among the reasons why he brought him to the club.
“I tried to sign him a couple fo years ago when he was at QPR. I couldn't get it done then but I’m delighted to get it done now – great age and from our point of view, his CV starting where he did.
“I was looking for competition in that area and he'll certainly provide that as a left centre-half.
“Just because he's out of favour somewhere else doesn't mean he doesn’r do a job for us. I’ve said all along I think there’s quite a bit of snobbery that goes with recruitment. We want players who will improve us and Jack will do that, his attitude is spot on.
“He wants to win and sees this as a fantastic opportunity. He's got that mentality of coming to a Premier League club and wants to get into a Premier League side.
“I don't think we've always had competition in that position, it's quite a difficult position to fill because of the charcteristics needed to play that position and certainly Jack has all the attributes needed.”