The 25-year-old striker joins the Hawks following his release from Portsmouth last month.
Although they have lost last season’s top scorer Jason Prior, Bradbury is happy with his four frontmen having last week added Dartford striker and National League South Player of the Year Alfie Pavey.
Kabamba brings energy and height and the manager believes his squad is coming together ahead of their return to pre-season training.
“He’ll bring experience but he’s still only 25,” Bradbury, who has taken Havant to back-to-back championships, told the the club’s website.
“It will be a very good signing with Alfie Pavey as well meaning we have an exciting front line with Alfie Rutherford and Matt Tubbs.
“There was quite a few after him but the location was key and the league that we are in which will hopefully give him a platform to get back into the professional game.”
Who will Havant face first? The National League fixtures are released on Wednesday July 4.