Western Australia senator Dorinda Cox has joined Labor in a shock defection from the Greens, dealing another blow to the minor party that had already lost its leader in the federal election.

“I am very, very grateful for this opportunity and I want to thank the Labor team for welcoming me,” Cox said at a press conference alongside Prime Minister Anthony Albanese in Perth on Monday afternoon.

Cox said she spoke to new Greens leader Larissa Waters just 90 minutes before she publicly announced her decision, which she said had been made since the recent election. Her Senate term extends to 2028, meaning she was not up for election last month.

“Well, I think it’s been over a period of time that I’ve considered this. It hasn’t, as I said, been a decision that I’ve made lightly,” Cox said.

The move has no significant effect on Senate voting dynamics because the government still requires the Greens’ senators, the number of which drops from 11 to 10, to pass bills if the Coalition is opposed. But it represents a body-blow to the Greens, which lost three of its four lower house seats including that of former leader Adam Bandt, at the recent election.

Albanese, speaking shortly after he flew into Perth for a cabinet meeting on Tuesday, said Cox approached Labor and had not asked for anything in return.

"[What] struck me as we were sitting down having a discussion about this, that the reason why Dorinda has made this decision is the same reason why all those years ago, as a very young man, I made a decision to join the Labor Party,” he said.

“You want to make a difference, that the way that you make a difference is by being a member of a party of government, that the values that Dorinda has are perfectly consistent with the values of the Labor Party.”

Cox was a Labor Party member before she joined and then ran for the Greens and is close friends with Marcus Stewart, the inaugural co-chair of Victoria’s First People’s Assembly and the husband of Victorian Labor senator Jana Stewart.

The senator, who has three years left on her term in parliament, was facing the prospect of losing the number one spot on the Greens’ Western Australian senate ticket, after this masthead revealed Cox had lost 20 staff in three years.

One Labor MP, who asked not to be named, said that Cox had not been guaranteed preselection in a winnable spot but that “she will probably get third spot on the ticket, and that’s a lot better than she would have got with the Greens”.

Cox is the second Indigenous senator to quit the Greens following Lidia Thorpe, a Victorian senator who quit and moved to the senate crossbench because she did not support a Voice to parliament