The body of Victorian Sergeant Matt Paton was recovered by Peruvian rescuers on Thursday local time in an abyss about 300 metres from a trail leading to Machu Picchu.
Sgt Paton fell from the Inca Trail on Wednesday afternoon while with a guided group headed to the ancient Inca citadel, one of the South American nation's most visited sites.
The 52-year-old's relatives said they were "shattered by this loss".
"It seems surreal at the moment - everyone is bereft," the family said in a statement on Friday.
"Family was the most important thing to Matt. He was dedicated to his family including his wife of 31 years and their three children. He adored his family. And we adored him."
The father of three had always wanted to travel to Peru and had been learning Spanish before the trip, they said.
"He was always up for an adventure and to learn something and to experience something new."
Victoria Police Chief Commissioner Mike Bush described Sgt Paton as a "wonderful, caring person".
"His colleagues and the entire policing family are devastated at the tragic loss," Mr Bush said in a statement.
"Matt loved travelling, exploring historic sites and cultures.
"He will be remembered for his selflessness, amazing sense of humour, extreme kindness and inclusion of all."
Peruvian authorities were investigating the circumstances of Sgt Paton's death, Victoria Police said.
His body has been taken to a morgue in the regional city of Urubamba for an autopsy.
Local police told ABC News he fell after tripping through a damaged security barrier in a difficult-to-access area of the trail.
Australia's Department of Foreign Affairs and Trade said it was providing consular assistance to the tourist's family.
"We send our deepest condolences to the family at this difficult time," the department said in a statement.
Machu Picchu, situated 2430 metres above sea level on the eastern slopes of the Andes Mountains, receives thousands of visitors daily.
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