Rodgers, 43, replaces Ronny Deila who stepped down at the end of a two-year spell which brought in two league titles and a League Cup crown but just frustration in Europe.
“Celtic Football Club is delighted today to announce Brendan Rodgers as the new Celtic manager. Brendan has agreed a 12-month rolling contract with the club,” said a Celtic statement.
Rodgers was previously in charge at Swansea, Reading and Watford while he spent three years at Liverpool before being sacked in October.
“I am absolutely delighted to be named Celtic manager,” said Rodgers.
“This is genuinely a huge honour 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.”