The Melbourne Rebels duo, who also played together in Queensland for the Reds, are the latest among top players to head to Japan to play club rugby after the country hosts the World Cup.
The Liners, who play in Japan's second-tier Top Challenge League, said that Genia will link up with the club after the World Cup, but Cooper, who was not named in the Wallabies' Rugby Championship squad, could move to Japan as soon as September.
Japan's domestic league season will begin in January 2020, which is later than usual due to the World Cup, which starts on Sept. 20.
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"I want to play soon as a member of a club with such history and tradition," Genia said in a statement on the club's website. "My aim is to do my best and, through my play, I would like to make this the number one team in Japan.
"I am honoured to be able to contribute to this team."
The Liners, who are based near Osaka, have never won Japan's Top League competition since it started in 2004 but did win the amateur All-Japan Championship three times between 1966-1974.
"I will work hard to take the team back to Top League," said Cooper. "When we reach the Top League, then I want to contribute more again at that stage.
"I want to challenge rugby in Japan and I can still contribute on the pitch. I appreciate that I was given this chance today."
Compatriot David Pocock will also return to Japan in 2020 and it was not just Australian players who have been enticed to Japanese rugby next season.
New Zealand's Kieran Read, Brodie Rettalick and Ryan Crotty will also be heading to Japan, along with South African number eight Duane Vermeulen. (Reporting by Jack Tarrant and Yoko Kono; editing by Sudipto Ganguly)
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