Cooper's decision follows Saturday's 3-0 home defeat by Carlisle United, a result which left Pools rooted to the foot of the table. The fact that this defeat came to a club below them was the final straw for the Pool Board.
The 47-year-old had been in charge of the Victoria Park side since May 2013.
"We would like to thank Colin for his efforts during the last 18 months," Hartlepool chairman Ken Hodcroft told the club website.
"We are glad that we gave him his break in management and would like to wish him every success in the future."
Hartlepool are winless in the last five matches, dating back to 6 September when they defeated Shrewsbury 2-0.