Speculation over the future of the Tigers manager has been rife for several weeks, with Adkins having been in discussions with the club hierarchy regarding a contract extension throughout the spring and early summer, with the offer first tabled by owners Assem and Ehab Allam at the end of March.
An impasse was recently reached with the 54-year-old having not received the reassurances he was seeking regarding the future of the club - prompting the decision for him to part company with the Tigers.
Adkins took over at the KCOM Stadium and helped the Tigers secure their Championship tenure in the second half of 2017-18 - finishing in 18th place.
Last season, he presided over a campaign which saw the club hint at play-off participation in the winter before finishing in 13th spot - against a backdrop of cost-cutting and constant off-the-field speculation about the future of the club.
Adkins' assistant Andy Crosby will also leave the KCOM Stadium at the end of the month with Hull saying recruitment for Adkins' successor "is already underway".
In a statement, Adkins said: "I’d like to thank all the staff and players, and in particular Andy Crosby, my assistant, for the hard work, camaraderie, togetherness and support they have shown me and wish them all good luck with their future careers.
"The unity the supporters have shown with the staff and players has also been very special. The fantastic relationship I have had with the fans makes leaving extremely difficult. I will take with me very special memories from the past 18 months.”
Speaking on social media, Adkins further added that he was leaving with 'a heavy heart', stating: "After much careful consideration I have decided that our futures are not aligned."