Rodgers took over at Parkhead in the summer of 2016 and won seven domestic trophies out of seven but left to join the Foxes on Tuesday evening.
Lennon was a successful manager at Celtic Park from 2010 until 2014 and now returns after spells with Bolton and Hibernian, having departed Easter Road at the end of January.
His first match in charge is against Hearts at Tynecastle this evening, with Celtic eight points clear of Rangers at the top of the Ladbrokes Premiership.
Celtic Chief Executive Peter Lawwell told the club website: “In bringing Neil back to the club until the end of the season, we have appointed a man who knows what it means to be Celtic manager and someone who knows how to win.
“We know he has the commitment and desire needed to face the challenges ahead. We are delighted to also promote John Kennedy to assistant manager and bring Damien Duff into our first-team management group. This will bring vital continuity and allow us to build on Brendan’s legacy.”
Lennon said: “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.”