The 43-year-old was sacked by Liverpool in October but has signed a 12-month rolling contract with the Scottish champion.
Brendan Rodgers has been appointed Celtic's new manager.
The 43-year-old has been out of work since he was sacked by Liverpool in October and has signed a 12-month rolling contract with the Scottish champion.
Rodgers said: "I am absolutely delighted to be named Celtic manager. This is genuinely a huge honor for me. I have followed Celtic all my life and to be given this fantastic opportunity and to be part of such a truly great football club is a dream come true.