Davey, who debuted as a 28-year-old at Parramatta in 2020, will join the Eels on an 18-month deal and be available for selection from next week.
His arrival comes as Parramatta prepare to spend the next two months without prop Reagan Campbell-Gillard, after scans confirmed a groin injury following Payne Haas' hip-drop tackle.
The Eels are also likely to lose Junior Paulo to NSW State of Origin duties, leaving Parramatta light up front.
Davey can play on an edge or through the middle and could also be used to relieve Ryan Matterson in the second row when he spends stints playing at prop.
His exit does create problems for Canterbury, however, with the Bulldogs in the midst of an injury crisis of their own with several forwards out.
"We know from Andrew's previous stint at the club, Andrew is someone who is ready for NRL and can play a role either at middle or edge," Eels head of football Mark O'Neill said.
"We are gaining a player who is of the highest character which is great for team culture and our Eels community."
Elsewhere, the Roosters have signed English flyer Lewis Murphy from the Super League.
Murphy scored 19 tries in 22 matches last year but the 21-year-old will miss the rest of this year after rupturing his ACL.
His impending arrival comes after the Roosters locked in Newcastle winger Dom Young for next year, while fellow winger Daniel Tupou is off-contract.
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