Cook, who left the Spireites' League Two rivals Accrington last October to take charge at the Proact Stadium, has extended his stay at the club until the summer of 2016.
Cook, 46, whose team are unbeaten in the league this season and top the table by four points, said: "My dad has been ill and he's been given the all-clear, which is great news for me and my family. To sign a new deal with the club caps a really great day.
"From the chairman down, everyone here has been really supportive. They gave me an opportunity to manage such a great club and the least I can do is repay their faith in me by signing a new deal.
"I've got a great relationship with our chief executive, who has been instrumental in everything I have done at the club. Managers always get the plaudits but without the staff behind you it would be an impossible job, so a big thank you to them as well.
"The fans here have been very supportive. Chesterfield has a strong fan-base, both home and away, and long may that continue.
"I'd also like to thank the players for their fantastic start to the season, but it is very early days. The players, like me, know there is a long way to go, but if they continue in the same sort of form, we will have a really good season."
Chief executive Chris Turner added: "I'm delighted that we've come to an agreement with Paul to extend his contract. Since the day he walked into the club, he's done a tremendous job. The standard of play is way above League Two standard.
"Managers who do well become prized assets and I thought it was important that we tied Paul down to a new deal so that he can hopefully take us where we want to go.
"It gives him ample time to continue the progress we've made this season. It's important for the people at the club to know that the person who is leading us from the front will be here for the next few years."