The 36-year-old played his last game in the Premier League for Sunderland in 2013 and has been working as an academy coach at his hometown club Ipswich.
"He came to training a couple of weeks ago, enjoyed it immensely and wanted to get involved," said boss Rick Andrews.
"From what I've seen in training, he's certainly very comfortable at this level," he told BBC Sport.
Bramble made 292 Premier League appearances over a 13-year period and appeared in the Champions League for Newcastle.
He is in line to make his debut at Felixstowe & Walton United on Saturday, and will also take on a coaching role with the Eastern Counties Premier Division side.
Stowmarket first-team coach Lee Norfolk and summer signing Scott Mitchell are also coaches at Championship club Ipswich, which is how the move came about.
"Some of my players are Titus' old school friends," added Andrews. "One sacrifice of professional football is not playing with your mates. He now has that opportunity.
"Will he play 40 games this season? Probably not. Will he play a fair chunk of games? Hopefully.
"I met him for the first time on Thursday because I'd been away, but he said he was taken aback by the quality some of the boys have here."
Former Newcastle and Ipswich defender Titus Bramble has joined ninth-tier Stowmarket Town on a one-year contract.