Genia is not expected to link up with his new team-mates until after the Rugby World Cup in Japan, though Cooper could move sooner having been omitted from the Wallabies squad for their Rugby Championship opener against South Africa.
Genia became just the tenth Australian to accrue 100 test caps when he ran out against England at Twickenham a year ago, only the second-ever scrum-half to achieve this after George Gregan.
The 31-year old is set to play a key role in the Wallabies' World Cup campaign before joining Kintetsu in Japan's second division next season.
The former skipper said he felt it was the right time to stand aside.
"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.
Flyhalf Cooper enjoyed a positive start to his lone season with the Rebels but suffered a slump in form, leading to his exclusion from the Rugby Championship squad.
"She [Olivia, his daughter] was probably one of the biggest reasons to leave and go to Japan and... retire from Test footy because I just want that time to spend with her", he said. "It seems like just yesterday I walked into Wallabies camp at aged 21 and now I'm 31".
Papua New Guinea-born Genia is now in South Africa with the Wallabies preparing for their Rugby Championship opener against the Springboks in Johannesburg on July 20.
"I think there's some very, very talented guys coming through and guys who are willing to work hard and have those ambitions".
The Melbourne Rebels duo, who also played together at the Reds, are the latest high-profile Australians to sign contracts with a Japanese team.
"I am very much looking forward to joining Kintetsu Liners".
"If I'm fortunate enough to be playing in the Test match there against Argentina in a couple of weeks that would be incredibly special and very emotional".