The former captain has agreed he will leave the club “in the interest of all parties”.
Davies said: “I am sorry that I could not achieve what I had set out to do from the day I joined.
“Football is an environment where you never know what’s around the corner; we go our separate ways with mutual respect and I am grateful for having had the privilege to be captain of Hartlepool United.
“I met some great people at the club, and the fans were great with me so I wish them, the staff and everyone else associated with the club every success in the future.”
Director of Football Craig Hignett told the club's website: “Andrew is a proper professional, a great lad and someone who we wish the very best of luck for the future,
“We are sorry it hasn’t worked out here but I’m sure that wherever he goes next he will be a success.”