The Victorian state parliament on Friday confirmed Senator-elect Thorpe to fill a casual vacancy caused by the retirement of former Greens leader Richard Di Natale.

She said it was a shame it had taken so long for an Indigenous person to be elected to represent her state.

"When I was growing up in public housing, the thought that someone like me could be in parliament was laughable," she said.

"My promise to the people of Victoria is that I will fight for you, no matter who you are."

Senator-elect Thorpe said her priorities would be achieving a treaty and justice for Indigenous Australians, ending economic disadvantage and tackling climate change.

She is expected to be sworn in when the Senate next sits on October 6.

Australian Associated Press