The 28-year Wigan defender 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."
Meanwhile, England keeper David James' representatives are in talks with Sunderland as Bruce considers his options in the wake of Craig Gordon's latest injury misfortune.