Shanae Edwards, also known as Shanae Brooke, had been teaching English in Tbilisi for about two years.

Brauer College principal Jane Boyle expressed her condolences to the 31-year-old's family.

"A number of our staff members have been upset by her death, which occurred in such tragic circumstances," Ms Boyle said.

"I offer my condolences to her family and the staff members also want to pass on their condolences."

Ms Boyle said counselling was available for any students affected by the former student's death.

Adam Griffin, who was friends with Ms Edwards when she lived in Melbourne, said he was devastated by her death.

"Shanae was one of the happiest, most optimistic and toughest people that I knew," Mr Griffin told The Standard.

"She was the type of person that never complained and had a fantastic work ethic - a real doer.

"I've felt shocked, sad and uneasy ever since I found out that she had been murdered. It's haunting."

The 31-year-old was reported missing on July 30 after failing to return from a hike in Mtatsminda park near Tbilisi.

Georgian authorities said her body was found the following day and have launched a criminal investigation into her death.

"As a result of several hours of intensive search and investigative activities, the officers of the Ministry of Internal Affairs found the female body on the slope of Mtatsminda," the ministry said in a statement.

"Within the frames of the ongoing investigation, appropriate forensic examination will be appointed. All necessary operative and investigative activities are underway."

An officer from the Australian Embassy in Turkey has travelled to Tbilisi "to liaise with Georgian authorities", a Department of Foreign Affairs and Trade spokesman said.

Local news organisation Agenda.ge reported one of Ms Edwards' friends received a "disturbing call" while she was on the hike.

In a post shared to a Tbilisi Expats Facebook page, Emily Channon said Ms Edwards had called a friend "while she was being attacked and screaming for help".

Tributes have been posted on social media in the days since her death, with Ms Edwards remembered as a "kind and giving adventurer".

"Shanae was always up for an adventure, so kindhearted to those around her, full of laughter and a shining light. I lack the words to fully express what I feel however I only have love for her," Sarah Richards posted in a tribute on Facebook.

Ms Edwards' friend Nat, who lives in Melbourne, said she was "heartbroken".

"And that doesn't even come close to how shattered I am that this has happened to you," she said on Facebook.

"You were the strongest woman I know, an incredible human being, always the life of the party, always radiant and positive no matter what life threw at you!"

The Melbourne woman fostered several kittens, and her friends have called out for people in the Tbilisi area to adopt them.

"She was taking care of 4 kittens and their mom cat from the streets. Her friends know HOW she loved them!" Lina Kha said in a Facebook post.

DFAT said it was providing consular assistance to Ms Edwards' family.

- Australian Associated Press