Cattermole completed his switch to the Stadium of Light on Wednesday after weeks of speculation in a £6million deal which will see him team up with former boss Bruce once again.
But Wigan boss Roberto Martinez has suggested the midfielder was unsettled by Sunderland's public pursuit which ultimately led to him leaving the club.
However, Bruce believes his new club went about the transfer in correct manner and insists Wigan were always willing to do business.
"It was no secret that we'd put in a bid three or four weeks ago and, contrary to reports that we'd unsettled Lee, I was encouraged after speaking to Roberto," said Bruce.
"He didn't dismiss it totally if we could get to the right sort of figure. There was always an element that gave me food for thought that it could be done.
"Roberto wants to add a few players of his own and he obviously used the situation to get some money in for players, which is fair enough and something all managers do.
"I have huge respect for the chairman, Dave Whelan, and everybody at Wigan and the last thing I wanted to do was go back there and disrupt anything.
"Once I got encouragement, I pursued it and didn't let it go. A couple of weeks ago I think Roberto had changed his mind and wanted to keep Lee.
"But then it was ongoing and, in the end, we got to the finish. We're just delighted that we've been able to bring the boy here.
"I try to treat every manager with respect. We know it's difficult these days, but as managers I always think we should call the manager first.
"I made the call to Roberto six weeks ago and I was encouraged that he might use the money to go and strengthen his team. Once I heard that, I thought, 'Let's see what develops'."
Cattermole joins the new-look setup at the Stadium of Light in a busy summer which has seen Bruce spend almost £25million on five signings.
The 21-year-old joins Darren Bent, Fraizer Campbell, Lorik Cana and Paulo Da Silva amongst the new signings as Bruce aims to bring the club up to a new level.
"The phone bill is astronomical and I'm dizzy with it! I'm delighted with what we've done. Now I just have to make it work and hope that they can gel."
Meanwhile, Paraguayan defender Da Silva has finally been given permission to play in England after being granted his visa and is expected to join up with the squad before Saturday's Premier League opener at Bolton.
"We seem to have forgotten about him. He was my first signing and we thought it was plain sailing but then we had to send him to get his visa stamped," said Bruce.
"He's been holed up in Mexico for 19 days, but he's got his visa now so we'll welcome him."