Wigan defender Bramble, 28, was in Portugal at the Black Cats' Algarve training camp on Thursday putting the final touches to his move to Wearside - with opinion divided back at home following his infamous blunder-plagued spell with derby rivals Newcastle.
However, Bruce, who worked with Bramble during his time with the Latics, is confident he would be able to reproduce his best form at the Stadium of Light.
He told the Sunderland Echo: "Look, I thought long and hard about signing him, long and hard because I knew it might be a difficult one for Sunderland fans and for him, but the great thing is that the lad's got plenty of bottle.
"He wanted to come here, he wanted to play for me and Sunderland, and I feel sure that Sunderland fans will recognise that and give him a fair crack of the whip. At the end of the day, Sunderland fans want the same as me and the same as Titus Bramble, which is success for this club.
"If Titus shows - as I think he will - that he can make us better, then I don't think supporters will have a problem accepting him. The easiest thing would have been not to sign him and to avoid any hassle, but I think he's a player who can genuinely improve us.
"He had a difficult start to his top-flight career. I think the move to Newcastle was too soon for him, it was too big a club at too tender an age and he's had his work cut out to shift the image of himself he created there."
Sunderland have also allowed defender Nyron Nosworthy to join Sheffield United on loan.
Blades boss Kevin Blackwell told the club's official website: "We made no secret of the fact that we were looking for defenders and that Nyron was a high priority of ours," Blackwell told the club's official website.
"Whilst we were - and still are - monitoring other alternatives, he fits the bill in every way, not least because we know what he can do and he fitted in well last season.
"He is a strong individual with bags of experience and he desperately wants to do well for this club because he knows the potential we have."