Sheridan has made a swift return to management after being sacked by Oldham in March. He succeeds Lee Richardson at Saltergate on a three-year contract.
New majority shareholder Dave Allen, who Sheridan knows from his time as a player at Sheffield Wednesday, was instrumental in the appointment of the 44-year-old.
Allen aims to bring Championship football to Chesterfield within five years and his plans for the club appealed to Sheridan.
"I wanted to get involved in football again as soon as possible but what excited me more than anything is this club is very ambitious and wants big things," said Sheridan. "They are moving to a new stadium next season and want to move forward and that is what I want to do as a manager.
"The club wants to be in the Championship within five years and that challenge appeals to me. They are in League Two at the moment but I believe, with a lot of hard work, I can get them out of this division and we can achieve those targets."