They have taken just four points from a possible 27 since Williamson's departure, Davies having so far failed to halt the post-Christmas slide that has seen City win just twice in 23 games, picking up a mere nine points out of a possible 69.
Davies, formerly Chester's head of youth, was keen to stress the support he has been given at board level.
"I'm extremely pleased to be given the job," he said. "Mr Vaughan has backed me all the way since I was originally appointed."
Chester travel to Shrewsbury on Saturday before ending their season with back-to-back home games against Stockport County and Macclesfield.