New Zealand and Australia are currently subject to lockdowns and the All Blacks cancelled two games last week including their Bledisloe Cup match in Perth.
But Queensland, largely free of coronavirus, has been deemed safe to host all four nations.
The new fixtures will be double-headers over four weekends from 12 September.
The Championship kicked off at Eden Park in New Zealand on 14 August, with the hosts thrashing the Wallabies 57-22.
South Africa then hosted two games against Argentina, winning both to top the table, before the competition was thrown into jeopardy as New Zealand's snap lockdown after a first coronavirus case in six months led to cancellations.
Three venues in Queensland will now stage the forthcoming rounds, except for the Australia-New Zealand game which is still set for Perth albeit with a date yet to be confirmed.
The Gold Coast will host New Zealand v Argentina and Australia v South Africa in a back-to-back double-header on 12 September in round three, as well as the round-six ties.
The other rounds will be played in Brisbane and Townsville.
"We thought last year was tough when we had to implement a Tri-Nations tournament in Australia with South Africa absent due to the pandemic," said Brendan Morris, chief executive of tournament organiser Sanzaar.
"But the current disruption caused by the Delta variant of Covid-19 has seen government authorities tighten up border biosecurity measures substantially.
"We had no option but to basically move the remainder of the Rugby Championship to Queensland."
Meanwhile, New Zealand Rugby has announced the reappointment of coach Ian Foster until the 2023 World Cup.