Former New Zealand rugby league international Hape takes over at inside centre from the injured Riki Flutey and he is one of four changes from the England team that started the final Six Nations game against France.
Hooker Steve Thompson and lock Tom Palmer both start after coming off the bench in Paris while there is a return to the England team for Leicester flanker Tom Croft.
Much to the surprise of the Wallabies, Wilkinson remains on the bench with Toby Flood retained at fly-half while Danny Care has held off the challenge from scrum-half rival Ben Youngs. Leicester hooker George Chuter and Northampton lock Courtney Lawes have both been included on the bench.
England are chasing their first victory over the Wallabies on Australian soil since the 2003 World Cup final - and only their third ever.
Hape will become the third former New Zealand rugby league international to play for England, following in the footsteps of Henry Paul and Lesley Vainikolo.
The 29-year-old, who won 14 caps for the Kiwis, has been on England's radar since switching codes to sign for Bath in 2008. Hape was in line to make his Test debut against Wales during the Six Nations, just weeks after qualifying for England on residency grounds, before falling ill on the eve of the game.
"I have been very impressed with him. He's a very smart carrier with the ball in hand. He's one of those guys that seems to have a bit more time than most, he's very composed," said England manager Martin Johnson.
Hape made his first England appearance in the non-cap game against the Barbarians at Twickenham before the squad left for Australia and has been preferred at inside centre to Bath team-mate Olly Barkley.
Elsewhere, Thompson came on tour as first-choice hooker after Dylan Hartley was ruled out of the five-match trip through injury while Palmer impressed off the bench in Paris at the end of March. Croft, a star of the Lions tour 12 months ago, returns to the back row after missing the Six Nations with a knee injury.
England side to face Australia: 15-Ben Foden, 14-Mark Cueto, 13-Mike Tindall, 12-Shontayne Hape, 11-Chris Ashton, 10-Toby Flood, 9-Danny Care; 8-Nick Easter, 7-Lewis Moody (captain), 6-Tom Croft, 5-Tom Palmer, 4-Simon Shaw, 3-Dan Cole, 2-Steve Thompson, 1-Tim Payne.
Replacements: 16-George Chuter, 17-David Wilson, 18-Courtney Lawes, 19-James Haskell, 20-Ben Youngs, 21-Jonny Wilkinson, 22-Mathew Tait