Greene, who has held the top post at the Canadian mail service since 2005, will fill outgoing chief executive Adam Crozier’s role at the beginning of July.
Royal Mail chairman Donald Brydon said Greene offers “energy, clear thinking and a proven leadership track record.”
Greene said she was “honoured to be joining such a great company”.
She led the privatisation of Canadian National Railway and the deregulation of Canada’s airline industry.
She will now be handed the task of taking Royal Mail partially private, as outlined in the Queen’s Speech on Tuesday.
She will also become the first female chief executive at the British postal service, and it will be the first time Royal Mail has been led by someone from outside the country.
Royal Mail also announced the appointment of Orna Ni-Chionna and Cath Keers, both of whom have extensive experience in consumer oriented businesses, as non-executive directors.