The right-back, 23, joined the League Two club in 2015 after a loan spell from Middlesbrough and his contract was set to expire in the summer.
Manager Keith Curle said: "David is a great lad but, with the additions we've made to the squad, he hasn't been able to get the game time he needs."
Atkinson had been on loan at Northern Premier League club Blyth Spartans and has now made the move permanent.
He only made two appearances from the bench for Carlisle this season.
Curle added: "He knows we're going through a progressive stage as a football club and he wants to give himself the best opportunity to kick his own career on."
Carlisle United and David Atkinson have parted company by mutual consent.