Hull-born Cooper joined the npower League Two side on loan in November and that deal was extended over the Christmas period.
The 21-year-old impressed Spireites boss Paul Cook during his 11 appearances for the club and has now moved to the Proact Stadium for an undisclosed fee.
Chesterfield chief executive Chris Turner said: "It is a tremendous signing for us because Liam has the potential to play at the highest level.
"We are delighted that he has chosen Chesterfield in preference to other options."
The move ends Cooper's long association with his hometown club. After progressing through the Tigers' youth ranks, he made his senior debut as a 16-year-old in a League Cup tie against Swansea in 2008.
His league debut for Hull came against Liverpool at Anfield and he went on to make 17 appearances for the Yorkshire club.