The Dutchman had been in charge of the Cobblers since last September but leaves them languishing in the relegation zone.
Sitting in 22nd spot in League One, they are two points off safety, but closest rivals MK Dons, AFC Wimbledon and Oldham all have games in hand.
"We are sorry to see Jimmy depart as he has worked very hard for us but felt a change at this point was in the best interests of the club," said Northampton chairman Kelvin Thomas.
"We thank Jimmy for his work as manager of Northampton Town and we wish him the very best for the future.
"We understand we are in a very tough spot and what the task in hand is, but I'm confident that the players, supporters and staff will all unite behind Dean and Jon for the remaining five games of the season.
"It has certainly been a challenging time for the club, but we need to look forward and put our full focus on these remaining five fixtures."