Chairman Colin Youngjohns said: "We did everything in our power to try to keep him, but Jan clearly felt that he had taken the team as far as he could.
"I am sure that everyone connected with the football club would like to join me in wishing Jan Molby and his family every success in the future. We would like to place on record or sincere thanks for the massive contribution Jan has made to the development of the club over the last three years.
"Jan Molby made the dream of Nationwide League football a reality in this town."
This leaves the door open for Molby to take up the post at Boothferry Park. Chairman Adam Pearson has expressed his interest in bringing the former Liverpool player to Hull.
He said following the announcement: "Nothing changes a great deal. Jan has put himself in the shop window. There are a number of clubs out there looking to strengthen the management team, of which we are one."
He confirmed that he would be inviting Molby for talks.