Thompson, 30, returns to Clitheroe where he didn't miss a game during the 2017/18 season.
Manager Phil Brown said: Brown said: “With Connor’s injury taking longer than first thought to heal we felt it important to seek someone who could come in and maintain the high level he has set.
“Initially Kai came in and has done that over the Christmas period and we are extremely grateful to him Burnley for agreeing to the loan at such short notice.
“However, the opportunity to sign a more permanent replacement in Chris was one we couldn’t turn down and I’m delighted to bring him back to the club.”
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