She will begin her five-year term on 14 September. She will be New Zealand's 21st Governor-General.
She will succeed former Chief of the Defence Force Sir Jerry Mateparae, when his term finishes at the end of August.
Dame Patsy is a lawyer who recently worked with Sir Michael Cullen on a review of New Zealand's intelligence and security agencies.
Prime Minister John Key said he welcomed the announcement that the Queen had approved the appointment.
"She is a passionate New Zealander, a well-respected businesswoman and a staunch supporter of our creative sector.
"She is thoughtful, articulate and has a brilliant legal mind. I am sure New Zealanders will be proud to have her as our Governor-General."