The former Sutton manager has signed a three-year deal at Westleigh Park, where he will be assisted by former boss Ian Baird.
Shaun Gale, who was former manager Lee Bradbury’s No2, will also be part of Doswell’s backroom staff.
Doswell spent 11 years in charge of the U’s before resigning earlier this month.
The 52-year-old replaces Bradbury as the Hawks’ boss following his departure on Easter Monday.
He will be tasked with returning the club to the National League following their relegation this season.