Aaron Cruden, who was called into the All Blacks' squad as replacement for the injured Dan Carter last month, will start at fly-half.
The two other switches are also behind the scrum, where full-back Israel Dagg returns after missing New Zealand's quarter-final victory over Argentina, and fit-again Richard Kahui replaces Sonny Bill Williams, who is on bench duty.
Williams' colleagues on the bench will include new Bath signing Stephen Donald after he joined the squad earlier this week when fly-half Colin Slade was ruled by injury.
In the pack, skipper Richie McCaw takes his familiar openside flanker's role, setting up a mouthwatering contest with Wallabies number seven David Pocock.
"The team was very happy with the way they played in the quarter-final win over Argentina," Henry said.
"It was a really intense battle, and that is what we needed heading into this weekend's match.
"We have been building slowly this week to be ready for Sunday, when we know there will need to be a further lift in intensity and physicality.
"It's a semi-final in the Rugby World Cup, and the team is excited by the challenge that lies ahead."
Australia triumphed in the last meeting between the countries almost two months ago, while both previous World Cup contests also went the Wallabies' way in the 1991 and 2003 semi-finals.
Team: I Dagg; C Jane, C Smith, M Nonu, R Kahui; A Cruden, P Weepu; T Woodcock, K Mealamu, O Franks, S Whitelock, B Thorn, J Kaino, R McCaw (capt), K Read.
Replacements: A Hore, B Franks, A Williams, V Vito, A Ellis, S Donald, S B Williams.
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