The 30 year-old was sacked by RA on Friday after a hearing over his anti-homosexual social media post last month, in which Folau, a devout Christian, uploaded an image on Instagram that said "hell awaits drunks, homosexuals, adulterers, liars, fornicators, thieves, atheists and idolators".
Folau, who had been warned by RA for similar comments last year, was found guilty of a "high-level breach" of the governing body's code of conduct and RA confirmed on Monday that the former Wallabies and Waratahs star had not appealed.
"The 72-hour window for Israel Folau to appeal his high-level code of conduct breach and sanction has expired," RA said in a statement.
"As Folau has not notified the panel of his intention to appeal, the code of conduct process has now formally concluded.
"With the code of conduct matter complete, Folau's employment contract will be terminated."
However, Folau issued a statement of his own that was widely circulated in the Australian media on Monday in which it was noted that he was "considering all potential avenues" with regards to further action against RA's decision.
"The last few weeks and, in particular, the last 72 hours have given me considerable opportunity to reflect and think about my future," Folau said. "I will not be exercising my right to appeal Rugby Australia's decision to terminate my employment contract."
"My decision not to commence Rugby Australia's appeal process is in no way an acceptance of the judicial panel's findings.
"I simply do not have confidence in Rugby Australia's ability to treat me fairly or lawfully throughout this process."
Folau, who has made 73 appearances for Australia, had previously said he would be willing to walk away from the sport but added in his statement: "I believe I still have a lot of rugby left in me."