Lennon has been on a six-month rolling deal since becoming permanent manager last summer, having been caretaker boss for the end of season 2009/10.
His representatives have been locked in talks with the club and a deal has now been agreed in principle.
BBC Scotland understands that Lennon will double his wages and earn just under £1m a year.
In his first full season in charge at Celtic, Lennon won the Scottish Cup but lost out on the Scottish Premier League title to rivals Rangers by a point.
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