The former Newcastle United defender replaces Neil Aspin at the International Stadium following his decision to accept the Port Vale job.
Watson, assistant to John Askey at Macclesfield Town, has been selected out of 50 applicants.
The number two has never made a secret of his desire to become a manager in his own right and has now been given that chance.
His first game in charge of the club will be this weekend’s 4QR FA Cup tie with Evo-Stik League Buxton.
Following the 2-1 weekend defeat to Bromley, chairman Richard Bennett suggested the club wouldn’t be hanging around.
“We have had a tremendous response,” said the International Stadium chief.
“Within the first few days we have 50 applicants and we have now a shortlist of seven. The quality has been excellent and we are delighted with that.
“Monday and Tuesday we are going to get some interviews going and may have an appointment before the FA Cup game at the weekend.”