It comes as North Queensland secure second-rower Heilum Luki through 2029 with a bumper contract extension.
Cleary's three-year deal returns his famous surname to Auckland; father and current Penrith boss Ivan is the Warriors' most-capped coach, leading the club to the 2011 grand final during his 154 games at the helm.
The younger Cleary, 19, played halfback for Penrith's SG Ball side this season, which ended in a seventh-placed finish for the Panthers.
He previously represented the Panthers in the Harold Matthews Cup as he came through rugby league nursery St Dominic's College, which counts Brad Fittler, Greg Alexander, Tim Sheens and brother Nathan among its alumni.
Cleary's signing comes only days after the Warriors announced they had signed talismanic Penrith prop James Fisher-Harris on a four-year deal that begins in 2025.
"The Cleary family has the strongest links with our club through Ivan's time with us, and it's a special thrill to sign Jett and have the Cleary name back with us," said Warriors chief executive Cameron George.
Cleary joins Chanel Harris-Tavita, Te Maire Martin and Luke Metcalf as halves options in Auckland next season, with 33-year-old starting halfback Shaun Johnson still undecided as to his playing future.
Cowboys star Luki now holds one of the longest contracts in the NRL after agreeing to a new extension.
Only Manly second-rower Haumole Olakau'atu is signed to his club longer than Luki, who joins the likes of Ezra Mam, Jarome Luai, Nicho Hynes and teammate Tom Dearden in being contracted through 2029.
The contract is a strong showing of faith in Luki after a horror run of injuries.
The 23-year-old, who has been in the Cowboys' system since he was 15, is currently sidelined with an ankle issue and has been restricted to 40 appearances since making his debut in 2021.
He is tasked with helping reinvigorate an inconsistent Cowboys side when he returns to the fold in round nine.
"(Luki) epitomises everything we value as a club," said Cowboys general manager of football Micheal Luck.
"He works hard at training, he's prepared to do the tough stuff on the field, and on top of that he is one of the elite back-row talents in the competition."
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