Boss Mark Fell swooped for the 25-year-old who has arrived at Giant Axe from NPL West Division side Workington.
Carroll will help the plug the void left by the departing Simon Wills.
Fell told the club’s website: “We’re really pleased to get it done, and Brad's one of a couple of key targets this summer.
"We’ve identified the areas we wanted to strengthen and improve and Brad was at the top of the list.
"So the fact that we’ve managed to get it over the line, especially since he’s had offers from elsewhere, says a lot about the direction we’re going in and the improvements we want to make, so we’re really pleased that we’ve got him on board.”
Carroll added: “I’ve played at Giant Axe a few times now and I’ve enjoyed the atmosphere and the ground itself every time I’ve been.
"I’m really looking forward to playing there week in week out and hopefully achieving success.
"At Workington, I loved the fans so I’m hoping I can bring that feeling and connection with me coming into this club. Overall, I’m delighted to be on board and looking forward to a tough pre-season and getting the season underway.”
Meanwhile, City have signed a three-year deal with local record label Fear Records who will sponsor the club’s home strip.