The Northern Irishman secured a 12-month rolling contract with Celtic.
The former Liverpool boss was given the Hoops job in recent days, signing a 12-month rolling contract with the Scottish Premiership giants.
The 43-year-old is one of the most high-profile appointments that Celtic have made, given his experience down south with helping the Reds mount Premier League title challenges, and earlier keeping Swansea City in the top flight.
But with a big profile comes plenty of attention - from the media and supporters on both sides of the Old Firm divide - on the Northern Irishman, something which Lennon can relate to having previously managed the Bhoys for four years until 2014.
As a result, Lennon feels that his compatriot would be wise to buy outside of Glasgow when it comes to house hunting, suggesting that Edinburgh would be the ideal location to live.
“The first thing he’ll have to deal with is the intrusion on his life. It’s a goldfish bowl,” Lennon told the Set Pieces.com.
“I think he may take a step out, live in Edinburgh and travel through (to Glasgow). That would be better for him. The intensity of the scrutiny you’re under is something he won’t be used to."
Of course, Rodgers will be tasked with fending off the challenge of Rangers and Aberdeen every season en route to Premiership titles, but he must also ensure Celtic qualify for the Champions League group stages.
Failure to achieve that and he might well meet the same end as his predecessor Ronny Deila.