Lennon, a former Celtic player and manager, will be in charge for the club's match against Hearts on Wednesday.
Rodgers, who took over at Celtic in 2016, replaces Claude Puel who was sacked by Leicester on Sunday.
Celtic, who have won consecutive titles under Rodgers, are eight points clear at the top of the Scottish Premier League.
Lennon joined Celtic as a player, from Leicester, in December 2000 and went on to make 304 appearances for the club.
The former Northern Ireland midfielder won five Scottish league titles with Celtic and steered them to two more as manager during his spell in charge from 2010-14.
Lennon parted company with Hibernian in January.
"I am absolutely delighted to be named manager of Celtic again. This is a club which has been such a huge part of my life already and it is an honour to be asked to return," Lennon told the Celtic website.
"I have given everything to Celtic as a player and manager already in my career and I am ready to do the same again."
(Reporting by Martyn Herman, editing by Pritha Sarkar and Toby Davis)
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