Hayne was told on Friday he had not made coach Ben Ryan's final squad for the Aug. 5-21 Games and is to return to Australia later this week.
Last year, Hayne defied the odds to make the 53-man roster of the NFL's San Francisco 49ers, less than a year after quitting Australia's top-flight rugby league competition.
"I had a meeting with Ben to discuss my future with the team and I was informed that my time has ended," Hayne, who quit the 49ers in May to pursue the Olympic bid, wrote on his Facebook page. "As much as I would have loved to go to Rio, I too knew I wasn't ready yet.
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"I used all my experience as a professional athlete and have tried everyday and in every way possible to make this team and make it better but unfortunately, time has been against me."
The son of a Fiji rugby league international, Hayne thumbed his nose at the critics in 2014 when he gave up a stellar career in Australia's National Rugby League, the sport's richest competition, for a shot at the NFL.
He left California after one season with the 49ers, with a modest record of appearing in eight games and one start as a running back under the now-departed Jim Tomsula.
He had 52 yards on 17 rushes and also caught six passes for 27 yards. He returned eight punts for 76 yards.
Hayne was included in the Fijian squad for the final World Sevens Series tournament in London in May and was used sparingly by Ryan as he struggled to come to terms with the intricacies of the shorter version of rugby and the fitness required.
By playing for Fiji in London, he is now ineligible to be picked for his native Australia at international level in rugby, though local media had reported he could be back in the sights of NRL clubs.
Local and European rugby clubs could also be an option for the 28-year-old, with the New South Wales Waratahs coach Daryl Gibson stating last week he would be interested in signing him for the 2017 season.
Hayne told News Corp last month he would also consider rugby offers from France and Japan.
(Reporting by Greg Stutchbury in Wellington; Editing by Peter Rutherford)
