The 28-year-old was named as one of the people thought to be caught up in the attack which killed seven and injured more than 40.
It emerged the Ms Boden, from Loxton, South Australia, had run to help people on the bridge.
Her family paid tribute to her saying: “Kirsty was loved and adored by her family, friends and boyfriend.
“She was the most outgoing, kind and generous person who loved to help people.
“Helping people was what she loved to do in her job as a nurse and in her daily life.
“As she ran towards danger, in an effort to help people on the bridge, Kirsty sadly lost her life.
“We are so proud of Kirsty’s brave actions which demonstrate how selfless, caring and heroic she was, not only on that night, but throughout all of her life. Kirsty – we love you and we will miss you dearly.
London terror attack – Kirsty Boden ran to help people injured on the bridge before she died
“We will not be making any further comments on this tragedy and ask everyone, especially the media, to give us the privacy we need to grieve away from the public eye.”
Ms Boden had studied nursing at Flinders University and had been working in London for some time.
Up to four Australians are said to have been caught up in Saturday night’s attack.
The family of Australian woman Sara Zelenak, 21, who has been missing since the London Bridge terror attack said they are "bracing for the worst", Australian media have reported.
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London Bridge terror: Scenes as armed police respond Sun, June 4, 2017
At least two people have died after being after reportedly being struck by a van on London Bridge on Saturday night.
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Armed police responding to the incident at London Bridge
A friend on Facebook said Ms Zelenak became separated on Saturday night as they ran for their lives.
Australia's ABC News reported a woman, who identified herself as Ms Zelenak's aunt Tara, spoke outside the family's home in Ormiston, near Brisbane, in Queensland on Tuesday.
"We are obviously very upset and emotionally distraught at this time. The family is trying to keep it together but bracing for the worst.”
Ms Zelenak's mother, Julie Wallace, told Australian radio station 97.3FM her daughter had been travelling in Europe since March and was working as an au pair for a family in London, caring for two young boys.
Ms Wallace said she had last spoken to her daughter on Friday afternoon when she said she was looking forward to meeting up with her parents in Paris in 28 days.
Asked how she felt when she was told her daughter was missing, Ms Wallace said: "Absolute terror, terror. Because we've been counting down the days to see her.
"I haven't seen her in three months. She went in March on this wonderful trip away, life experience thing, that I was encouraging her to do because life experience is so good."
She said Ms Zelenak had been at Westminster the day before 52-year-old terrorist Khalid Masood killed five in a car and knife rampage, and had planned to go to the Ariana Grande concert in Manchester, where suicide bomber Salman Abedi murdered 22 victims.
"Everything, she's just missed," said Ms Wallace, who added she was planning to come to London with her husband to look for her daughter.
Canadian Christine Archibald died in her fiancé's arms
James McMullan, 32, from Hackney, was last seen outside the Barrowboy And Banker pub
Ms Boden is the third person to named among the dead after three attackers ploughed into pedestrians on London Bridge and then stabbed people in Borough Market.
Canadian Christine Archibald, 30, was named as the first victim of the London Bridge terror attack after she died in her fiancé's arms.
Writing on Facebook, Cassie Ferguson Rowe said her younger brother Tyler Ferguson held his fiancée in his arms after she was hit by the terrorists’ speeding van on London Bridge.
She said: "Last night in London my baby brother lost the love of his life on the London Bridge.
"In a split second his entire life was ripped away from him. Hearing his painful sobs on the phone while he's alone trying to deal with this tears me apart.
Sadiq Khan leads sombre vigil for London terror victims Tue, June 6, 2017
London Mayor Sadiq Khan lead a vigil to commemorate the victims of the London Bridge terror attack. Hundreds attended the event outside London's City Hall
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London Mayor Sadiq Khan bows his head
James McMullan, 32, from Hackney, was last seen outside the Barrowboy And Banker pub and his sister said police have told her his bank card was found on a body at the scene of the attack.
Melissa McMullan told Sky News "While our pain will never diminish, it is important for us all to carry on with our lives in direct opposition to those who wish to destroy us and remember that hatred is the refuge of small-minded individuals and will only breed more.
"Words will never be able to match his essence, there will only ever be one James.”