Premier League - Bramble bailed over rape claim
Bramble "strenuously denies any wrongdoing", club chairman Niall Quinn said.
A Northumbria Police spokesman said: "Both men have been bailed pending further inquiries."
They will answer bail on December 2.
Quinn said in a club statement: "This has been a very difficult day for everyone at the football club, no one more so than Titus, who categorically refutes the allegations that have been made against him.
"He strenuously denies any wrongdoing and will be doing everything within his power to clear his name.
"I as chairman, and the club as a whole, totally support Titus in his efforts and we all hope for a swift conclusion to this matter."
Bramble, 29, and a second man were arrested early on Wednesday morning at the Vermont Hotel after a woman in her 20s phoned the police.
It was later confirmed that the second man arrested was Bramble's brother, Tesfaye Bramble, 30, who plays for Eastern Counties League Premier Division club Leiston, in Suffolk.
A spokesman for Northumbria Police said: "Police received a report of a rape of a woman at a city centre hotel in Newcastle in the early hours.
"Two men, aged 29 and 30, have been arrested on suspicion of rape."
Sunderland have yet to comment on the story and a hotel spokesman also refused to comment.
Bramble only joined Sunderland this summer from Wigan Athletic.
He is a former England U21 international who has also played for Ipswich and Newcastle.