Bramble's brother Tesfaye remains on police bail.
Sunderland AFC chairman Niall Quinn said: "Naturally the last few weeks have been difficult for Titus and I hope that those who condemned him without being in possession of the facts will now offer their apologies.
"From day one Titus categorically refuted the allegations made against him and the club backed him 100%.
"I'm delighted that this has now been resolved and Titus can continue his growing career at Sunderland Football Club."
A Northumbria Police spokesman said: "A 29-year-old man has been released and no further action will be taken.
"A 30-year-old man remains on police bail."