Former and current territory politicians heralded in the vote at Parliament House.
"The arc of history bends toward justice," ACT Chief Minister Andrew Barr said, quoting Martin Luther King Jr.
"We are humbled. It's been a long journey to get to this point," he said.
Mr Barr said consultation on legislation in the ACT will begin early next year, with a vote on the issue to be held at the end of 2023 or start of 2024.
Former NT chief minister Marshall Perron oversaw the legalising of euthanasia in the territory in 1995, sparking the federal bill that overrode the territories' right to do so.
Mr Perron says he was reflecting on the 1000 to 2000 NT residents who had been denied access to voluntary assisted dying while watching the legislation pass.
He said the passing brought an end to "25 years of democratic inequality motivated by religious zealots".
Senators cheered in the chamber on Thursday after legislation passed to repeal a 25-year-old law put in place by Liberal MP Kevin Andrews.
ACT senator David Pocock celebrated the bill's passing after months of advocacy and negotiations to bring it on for debate.
"This is on the back of a lot of advocacy, it's a historic moment," the independent senator said.
"People in our communities who have terminal diagnoses know this is unlikely something they'll have the choice to use but they want other people in the future to have that.
"That's an incredibly brave thing to do, to come forward and tell your story."
Coalition senators Jonno Duniam and Nampijinpa Price tried to amend the bill to ban euthanasia for people under the age of 18 as well as review the types and regulations of medication used.
But Finance Minister Katy Gallagher said it was a simple repeal bill, nullifying the legislation which upholds the ban.
The ACT senator said any safeguards surrounding how euthanasia would be administered would be a matter for the territories' Legislative Assemblies.
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