Curle was sacked by Mansfield earlier this season following an internal investigation.
He replaces caretaker boss David Bell, who has been in charge since Ian Rush resigned from his post.
Rush himself had only arrived at the club in August, after former boss Mark Wright was sacked on the eve of the new season after revelations of an affair with a former player's wife.
Chairman Stephen Vaughan also spoke to John Hollins and Vauxhall Motors boss Owen Brown before opting for former Mansfield boss Curle.
"I never had any doubts as to my choice from the minute I met Keith. The board and I feel that his appointment will pay dividends for this club," said Vaughan.