The Senate passed the legislation on Tuesday with amendments that beefed up the powers of the inspector who provides oversight of the commission.

The amendments were ticked off in the lower house on Wednesday with multi-party support.

Crossbenchers failed in their attempts to lower the threshold for public hearings to be held, arguing there needed to be transparency about what was being investigated.

The opposition and government teamed up to keep the “exceptional circumstances” test before a public hearing can be held.

Prime Minister Anthony Albanese said it was a win for honesty, accountability, integrity and trust.

“Today we take an important step to rebuild trust in government, our public institutions and our democracy,” he told parliament.

“It represents an end to rorting and waste.”

The National Anti-Corruption Commission will be able to investigate conduct in the Commonwealth public sector, which can extend to MPs and their staff, as well as government employees and contractors.

The commission will operate independently from government, and will be able to start inquiries by itself, or via referrals from members of the public.

It will be overseen by a parliamentary joint committee which will require the commission to provide information about its work.

Albanese welcomed the fact the opposition, crossbench and government had worked closely to improve the bill and pass it.

Independent MP Helen Haines, who had long advocated for a federal integrity body, said the passing of the bill was a happy day for democracy.

“We need to hold true to integrity in all its forms, we need to make sure that when those who hold public office do wrong, that they must be accountable for doing so,” she told reporters in Canberra.

“We have got across the finish line, but the work of integrity is never done.”

Haines said there would not be a shortage of work for the commission once it was set up.

Greens senator David Shoebridge said there would be a key test for the NACC on whether it would define pork barrelling as corrupt conduct.

“Most Australians were disgusted by the use of public money for blatantly partisan purposes,” he said.

“When the NACC is up and running, I’m sure it won’t just be my office and my party that has a number of matters to be referred.”

Greens leader Adam Bandt said there would be a long list of cases the commission would examine.

“I don’t think that the new corruption commissioner, if they’re appointed soon, is going to have much of a Christmas break because there’s going to be a big workload after 10 years of one of the worst governments that we’ve seen,” he said.

The Australia Institute’s National Integrity Committee, made up of retired judges, welcomed news of the commission passing but still had issue with the high bar for public hearings.

“The NACC should not be limited to holding public hearings in exceptional circumstances only, and we recommend that the parliament revisit the commission once it is operational,” the group said in a statement.

– AAP