Cuckoo will star Samberg as an idle young man who marries a British girl, according to The Independent.
The character will come into conflict with his new wife's overprotective father, played by stand-up comic and actor Davies.
In addition to his Saturday Night Live work, Samberg has appeared in such films as 2007's Hot Rod and 2009's I Love You, Man. He is also a member of musical comedy troupe The Lonely Island.
Davies - best known for playing Mr Gilbert on The Inbetweeners - frequently appears as a panellist on the BBC's Mock The Week and previously starred in BBC Three series We Are Klang.
It was announced last year that stand-up comic Jack Whitehall will appear in new BBC Three comedy Bad Education.
The Fresh Meat star will play Alfie, who is described as "the worst teacher ever to grace the British education system".
BBC Three controller Zai Bennett described the two shows as "where I want BBC Three comedy to be".
"I can't overstate the importance of comedy," he said. "If you get comedy right it can define your channel."
> Rob Riggle joins comedy show World Series Of Dating on BBC Three
> Jennifer Saunders joins new BBC Three sitcom Dead Boss
Watch Greg Davies discuss his stand-up comedy with Digital Spy below: