Rugby Australia (RA) said on Saturday that Rodda and the teammates, flyhalf Issac Lucas and lock Harry Hockings, had been granted the release.
"Rugby Australia and the Queensland Rugby Union (QRU) have made the decision to release the three players from their contracts, effectively immediately," RA interim Chief Executive Rob Clarke said in a statement.
The trio were "stood down" by the Reds on Monday after refusing to accept salary reductions or sign up to the government's JobKeeper programme.
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RA implemented a 60% pay cut for its players last month after tense negotiations with the Rugby Union Players' Association amid the governing body's financial struggles that have been exacerbated by the novel coronavirus outbreak.
It furloughed about 75% of its staff in March.
"As everyone is aware, the impacts of COVID-19 have been felt in every country, across every industry, and rugby is no exception," Clarke added.
"As a result, the game collectively took the difficult but necessary action to stand down over 70% of the entire rugby workforce, which equates to over 150 workers.
"At the same time, 189 professional rugby players in Australia accepted reduced pay for an interim period to enable the game to navigate this unprecedented situation."
The players' agent, Anthony Picone, said on Friday that RA and the QRU had "no legal basis to issue the stand-down notice" and the players were just trying to protect their livelihood. (Reporting by Greg Stutchbury; Editing by William Mallard)
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