The 25-year-old, who played under Spireites boss Paul Cook at Irish club Sligo Rovers, is out of contract at the end of the season and recently turned down the offer of a new deal with the Scottish Premier League outfit.
Doyle has signed a pre-contract agreement with Chesterfield and will be reunited with Cook following Hibs' Scottish Cup final appearance against Celtic at Hampden Park on May 26.
Doyle helped his team earn their place in the final by coming off the bench to score the equaliser in Saturday's thrilling 4-3 comeback victory over Falkirk in the semi-final.
Hibernian were 3-0 down after half an hour but the Irishman netted their third goal in a rousing revival before Leigh Griffiths fired in a spectacular extra-time winner.
Doyle joined Hibs from Sligo Rovers in December 2011 and has scored 12 goals in 50 appearances in all competitions for Pat Fenlon's side.