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The Oxford-bred five-piece embarked on an international tour after releasing their eighth studio album, The King of Limbs, last year.
The just-announced show at Vector Arena in Auckland on November 6 is the band's first in New Zealand since 1998.
They will follow that up with five shows across Australia.
Rumours the band would be returning to New Zealand began last month when Kiwi singer-songwriter Connan Mockasin saying he'd be coming back to New Zealand with Radiohead.
He said: "I won't be coming home for camp [A Low Hum] but will be with Radiohead later in the year.''