Cleary was sensationally sacked by Panthers supremo Phil Gould on Monday.
The former NSW State of Origin mentor said he believed Cleary needed a break from coaching.
"Understand that we did not advertise this position. We did not accept applications and we interviewed no other candidate. We are delighted he has accepted our invitation to be the new head coach at out our club," Gould said.
Griffin spent four years at Red Hill and was moved aside ahead of the 2015 season to make way for returning supercoach Wayne Bennett.
Cleary spent four seasons at the foot of the mountains after leaving the Warriors following their 2011 grand final loss to Manly.
He was brought to Penrith with much fanfare by Gould and led the Panthers to the preliminary final in 2014.
This year, however, the Panthers only narrowly avoided the wooden spoon courtesy of a final-round win over last-placed Newcastle.
- AAP