Greene ran Canada Post before taking on the job in the UK, perhaps inspiring Mark Carney to also make the leap to the bigger market, and is currently an EasyJet director.
She will replace Paul Tellier, a fellow Canadian civil servant-turned business executive, who has been a Rio director since 2007.
Greene's time at Royal Mail has spanned privatisation, major layoffs and the rise of parcel delivery thanks to internet shopping.
Outgoing Rio chairman Jan du Plessis said the Canadian-swap would help the company.
"[Moya] will further strengthen board discussions and bring an invaluable insight of both the private and public sectors and, crucially, how they interact with each other," he said.
"I would like to thank Paul for the significant contribution he has made over the last decade and for the wise counsel he has offered me and the board.
"With Paul stepping down, Moya will ensure that the board maintains a strong Canadian voice, reflecting the importance of Canada to Rio Tinto."