McClennan has signed on a two-year deal through to the end of the 2013 NRL season.
The former Kiwis coach has never been in charge of an NRL team but has a successful record at the international level and in the Super League.
McClennan, 49, coached New Zealand to Tri-Nations success in 2005 before finishing with a 7-9 record with the Kiwis.
He then guided Leeds to back to back Super League titles in 2008 and 2009. He is currently working as football development manager for Auckland Rugby League.
Cleary will leave the club at the end of the year to take over as head coach of the Penrith Panthers following six seasons with the Warriors.