Familiar face returns to Ashton Town
Dempsey had been in charge at Widnes, after a short spell with Atherton Collieries.
He rejoins Town for a second time after the shock departure of Glynn Hurst last month.
Town chairman Mark Hayes said: "Demps left us in third place in the league after a promotion and a cup win.
"We work very well together and I am truly excited to be doing it again.
"Huge thanks to Widnes for allowing the approach and of course Terry Smith, who leaves us as interim manager with two wins and a draw.
"This quite simply and definitely a case of unfinished business. Huge thanks to all applicants."
Dempsey added: "Really pleased to be coming back to Ashton Town.
"There is a massive sense of unfinished business and I’m ready to help the club progress!
"Thanks to Mark for trusting in me and asking for me to return."
Interim boss Smith tweeted: “Disappointed not to get the manager position. Good luck for the season boys.”