The minor party struck a deal with the government on Tuesday to pass curbs to negative gearing and the capital gains discount within the next two weeks.
The Greens also secured a handful of amendments to the tax changes.
The coalition strongly opposes the tax changes, saying they will hurt young home buyers and small businesses, leaving the Greens as the only path for Labor to get the bill through the Senate.
Under the agreement, the government will close a loophole where people can buy property through self-managed super funds (SMSFs) to avoid the CGT increase.
SMSFs will be banned from using limited recourse borrowing arrangements, which allow trustees to borrow for a property while protecting the rest of the fund's investments from lenders if they default.
The Greens have argued closing the loophole prevents investors flocking to SMSFs to purchase tax-advantaged properties.
"Multiple inquiries have raised concerns that these arrangements raise risks for superannuation investors ... and limiting new arrangements going forward will help protect people's savings," Prime Minister Anthony Albanese, Treasurer Jim Chalmers and Finance Minister Katy Gallagher said in a joint statement.
Super funds are protected from the tax changes, which will remove the 50 per cent discount on the capital gains tax for established properties and replace it with indexation of the cost base and a 30 per cent minimum tax.
The changes will be extended to all assets, including businesses, although the government has announced a carve-out for innovative firms to placate the startup sector, which has complained it would be uniquely impacted by the new arrangements.
The bill also includes abolishing negative gearing for established properties, a $250 per year tax offset for workers and a standard $1000 deduction for work expenses.
As part of the Greens' deal, the treasurer will also have his powers to extend the 50 per cent discount to more assets reined in.
Greens leader Larissa Waters said the package was a step in the right direction, but the government missed an opportunity to actually fix the housing crisis by grandfathering arrangements for existing investors.
"It could have been so much better, but it is a small step in the right direction," she told reporters in Canberra.
"We will not stop fighting for young people, and for all Australians, to be able to afford a roof over their heads."
In exchange for the Greens' support of the tax changes, the government also agreed to extend the NDIS inquiry by eight weeks.
Labor has made a number of amendments to the NDIS bill, curbing ministerial powers and improving transparency.
But the Greens say even with those changes, they will still oppose the bill.
A snap parliamentary inquiry's final report on changes to the $56 million NDIS scheme was due to be tabled on Tuesday after two extensions were granted.
However, an interim version is expected to be tabled instead, with the committee now set to deliver a final report by August 14.
The proposed NDIS overhaul would boot 160,000 people from the scheme to rein in spending and leave thousands more with less funding.
Delaying the report would grant more time to build pressure on both Labor and the Liberals to withdraw support for the bill entirely, the Greens said.
The government has also agreed to amendments that will limit ministerial powers to cut recipients' budgets, ensure greater transparency on automated decision-making and prevent recipients from being forced to undergo restrictive practices to gain access to the NDIS.
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