General Cosgrove will replace Quentin Bryce when her term ends in March, taking over as the Queen's representative in Australia.
The 66-year-old Vietnam veteran admitted he had once believed he wasn't suited to the role, but that times change and duty calls.
Former Prime Minister John Howard welcomed the appointment as a "magnificent" choice, praising Peter Cosgrove as a man who has a "common touch" as well as "strength and dignity".
"One of the things that has impressed me about the man is his capacity to mix with all sections of the Australian community. He really does have that great capacity.
"I've seen him in a military situtaion, with the men and women of the ADF, and I've seen him in other situations. He has the common touch, but he has strength and dignity and that's just the right combination."
"If you foresee that there's a call to arms, so to speak, as an old soldier you just get on with it," he told reporters in Canberra on Tuesday.
He will also assume a role familiar to a man who has spent his entire life in the military - as commander in chief of the Australian Defence Force.
Given his military pedigree, General Cosgrove wasn't surprised people would assume he would play a major role in this year's Anzac Centenary celebrations.
But the self-declared "staunch Australian" said he wanted to go on a voyage of discovery and learn everything he could about people in everyday life.
"The military is a very small proportion - albeit a precious one - of our community," he told reporters in Canberra on Tuesday.
"My wife and I will make sure we visit widely."
He expressed a desire to visit indigenous communities with new Australian of the Year Adam Goodes, and pay close attention to theissues affecting ordinary people.
But don't expect him to weigh in on political issues of the day.
General Cosgrove said he would be following his predecessor's example of trying to reflect the will of the Australian people without being a political participant.
"I think your responsibility is to shine light, but not to generate heat," he said.
Prime Minister Tony Abbott paid tribute to General Cosgrove's lifetime of service, saying he couldn't think of anyone better for the job.
"I am confident that in this new role he will continue to deliver to a grateful nation leadership beyond politics," he said.
Acting opposition leader Tanya Plibersek praised a man who has dedicated his entire adult life to serving his country.
"General Cosgrove reflects the best of Australia and its people," she said.