Dempsey, 32, takes up the position having left his role on the first team coaching staff at Atherton Collieries under Brad Cooke last month.
He replaces Craig Davies at Widnes, who left the club in July to take up the managerial position at Prescot Cables.
He previously managed Ashton Town up until December 2019, leaving Town in fourth in the North West Counties Division One North having guided the club to promotion back to the North West Counties from the Cheshire League in 2018.
"Thanks for the opportunity," he shared on social media.
"I'm really looking forward to working with the players and management team in helping the club progress. Thanks to Ackers and Towey for giving me the opportunity."