The former Newcastle defender travelled to the Black Cats' Academy of Light training ground yesterday afternoon to discuss personal terms and undergo a medical.
Bramble is currently nursing a broken foot but will be fit to resume full training in around a fortnight. The injury is not expected to hinder his medical on Wearside.
Talks are understood to have progressed well, and Bramble is expected to be confirmed as Sunderland's most expensive summer signing to date.
His return to the North-East has occurred at breakneck speed, with Bruce only tabling a formal offer for his services on Monday after another of his leading targets, Heiko Westermann, joined Hamburg.
Latics chairman Dave Whelan has criticised Sunderland's transfer dealings in the last two transfer windows, each of which has seen the Black Cats launch an unsuccessful pursuit of full-back Maynor Figueroa.
However, with Wigan boss Roberto Martinez hoping to raise funds to make signings of his own this summer, Whelan was quick to grant Bramble permission to travel to Wearside.
The 28-year-old's arrival will split Sunderland supporters, many of whom remember him as the gaffe-prone centre-half who made more than 150 senior appearances for Newcastle between 2002-07.
The Ipswich-born defender was already on Wigan's books when Bruce moved to the DW Stadium in 2007, and his career was transformed under the current Sunderland boss.
He was voted Wigan's Player of the Year in his first full season with Bruce and has made a total of 104 appearances for the Lancashire club.
He was the subject of tentative interest from Sunderland last summer, only for Wigan officials to quickly rule out any prospect of him leaving.
However, the situation has changed and, provided there are no problems with the result of his medical, he should be confirmed as a Black Cats player in the next 24 hours.
His arrival would place a huge question mark over the future over Anton Ferdinand, and would also suggest Bruce has admitted defeat in his pursuit of both Sol Campbell and Nedum Onuoha.
Campbell has held face-toface talks with Sunderland officials, but is understood to have expressed a desire to speak to Newcastle when he returns from his honeymoon at the start of next month.
Onuoha has been a leading target all summer, but Manchester City's £8m valuation of the youngster has proved an insurmountable obstacle to any deal.
As well as chasing Campbell and Onuoha, Bruce also tabled a £4m bid for Westermann last month, but after Schalke rebuffed Sunderland's offer, the Germany international completed a £7m move to Hamburg yesterday.
Bramble will become Sunderland's fifth summer signing if he puts pen to paper later today, following Cristian Riveros, Simon Mignolet, Ahmed al-Muhammadi and the returning Bolo Zenden to the Stadium of Light.
Zenden signed a new deal with the Black Cats despite having threatened to leave after starting just one Premier League match in the whole of last season.
The Dutchman, who scored Sunderland's only goal in their pre-season victory at Darlington last weekend, is determined to improve his appearance record next term, and insists he will not be satisfied with a handful of substitute appearances.
I had the option to come back for another year if I played 50 per cent of the games, so I have come back,
said Zenden. But I want to play more than last year.
I wasn't happy with the amount of football I played.
It was very frustrating spending time on the bench. I don't want to be someone who just passes on my experience in training, I want to be playing.
Sunderland play the opening game of their Portuguese tour this evening when they take on Brighton in Albufeira (ko 9pm).
Martyn Waghorn could make a surprise appearance against the Seagulls after flying out to join in training yesterday.
The striker has received the all-clear after injuring his knee in last week's 2-1 win over a Munster XI.
Nyron Nosworthy will not be involved, however, after agreeing a season-long loan with Sheffield United yesterday.
Sunderland had hoped to strike a permanent deal for the defender, who spent the second half of last season on loan at Bramall Lane, but have agreed to another temporary arrangement.