Harry, Prime Minister Scott Morrison, and three Invictus Games athletes started the climb.
Harry and his party took 13 minutes to reach the summit of the bridge.
Under sunny skies, Harry swapped the New South Wales standard for the Invictus flag at the top of the bridge, which sits 134 metres above the water.
Among those joining the duke and prime minister Scott Morrison at the summit were three Australians who will be showing what they are made of at the Games, which open on Saturday.
Luke Hill, a swimmer, who was deployed to Timor-Leste three times, Captain Ruth Hunt, who will take part in the indoor rowing and swimming, and Peter Rudland, who was deployed to Cambodia, twice to Iraq, twice to Timor-Leste and Afghanistan, and will compete in the cycling and wheelchair rugby, all made their way to the top of the bridge for the flag ceremony.
Also climbing the structure built in 1932, was Gwen Cherne, who is an ambassador for the Games.
Her husband Peter Cafe served in Cambodia, Afghanistan and Iraq and took his own life in February this year. Since then, Ms Cherne has become an Invictus and War Widows Guild ambassador.