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Australia and the social media group have been locked in a standoff for more than a week after the federal government introduced legislation that challenged Facebook and Alphabet Inc's Google's dominance in the news content market.
Facebook last week blocked all news content and several state government and emergency department accounts.
But after a series of talks between Frydenberg and Facebook chief executive Mark Zuckerberg over the weekend, a concession deal has been struck.
Australia will offer four amendments, including to the mechanism for final offer arbitration, which a Facebook executive told local media was a sticking point for the company.
"We are satisfied that the Australian government has agreed to a number of changes and guarantees that address our core concerns about allowing commercial deals that recognise the value our platform provides to publishers relative to the value we receive from them," Facebook said in a statement posted online.
The issue has been widely watched internationally as other countries including Canada and Britain considering similar legislation.
Australian Competition and Consumer Commission chair Rod Sims, the main architect of the law, was not immediately available for comment.
At a speech earlier on Tuesday, Sims declined to answer questions about the standoff on the grounds that it was before parliament.