Bruce has also been linked with a move for Bramble's Latics team-mate Charles N'Zogbia, another former Magpie, who is attracting interest from Marseilles.
After sitting in the dugout for the 1-1 draw against Brighton on Wednesday, Bramble is at the Wearsiders' pre-season training camp in the Algarve to agree a return to North-East football following his three-year spell at Wigan.
Bruce insists that Bramble is a vastly improved player from the sometimes hapless figure who featured in Newcastle colours.
The Sunderland boss dismissed suggestions that the Stadium of Light faithful would struggle to accept Bramble as one of their own.
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. And 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, said Bruce.
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.
But he has been a Premier League defender for ten years now. Two of those were for me, when he was terrific and if he reproduces that sort of form, Sunderland fans won't have a problem with him.
Titus wants to come. He could quite easily have said no', but he wants to come to Sunderland and I admire him for that.
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.
His problem has always been his concentration levels but that's something we improved out of sight at Wigan.
I've got a player that I was quoted £5m for last summer, at a fraction of a price this time around, he said.
But, more importantly than that, I've got a player who has been there, seen it and done it in the Premier League over the last decade.
We've brought in some players who have lacked Premier League experience, but that can't be said about Titus.
Meanwhile, Argentina international right-back Marcos Angeleri is expected to finally complete his £2.7m move from Estudiantes after the player's representative confirmed that clearance has been received that allows the 27-year-old to qualify for an Italian passport.
Defender Michael Turner has joined Sunderland's growing injury list and is a doubt to face former club Hull City in Portugal tomorrow after being forced to withdraw from training with a thigh muscle injury.
He joins Andy Reid, George McCartney, Lee Cattermole, David Meyler and Craig Gordon on the treatment table.