Doswell announced his resignation from National League Sutton United last week, ending his 11-year stint at Gander Green Lane.
His stand-in at the U's Ian Baird also links up with him at Westleigh Park.
"I'm really pleased. The goal is to get us back into the National League," Doswell told the club's official website after signing a three-year-deal at the Hawks.
"The hard work has started today, I'm looking forward to it.
"My job is to put smiles back on people's faces and I'll be involved with that whole aspect in and around the club."