The deal, which closes a so-called loophole in the federal budget's changes to the capital gains tax discount, will ban funds from borrowing to buy residential properties, meaning they can not avoid changes to the capital gains tax discount.
The Greens will vote for the budget bill in its entirety and it is now likely to pass the upper house before winter break starts next week.
But for the government, passing the controversial bill before the fortnight is up may not be enough to stave off the rise of One Nation's rise in opinion polls.
Treasurer Jim Chalmers cited recommendations made by former Commonwealth Bank of Australia chief executive David Murray to then-Liberal treasurer Joe Hockey in 2014 to justify sparking a deal with the Greens at a time when One Nation eclipses Labor in the polls.
The legal practice known as limited recourse borrowing arrangements (LRBAs), which allows self managed super funds to get a loan for buying assets in specific circumstances, will become all but obsolete as a result.
Fund managers were disappointed the government "agreed to Greens' demand".
"Review are after review has found LRBAs pose no material risk to the superannuation system," Self-Managed Super Fund Association chief executive Peter Burgess said.
"The problem is not the borrowing structure itself, but the conduct of those who aggressively market unsuitable property investments and make unrealistic claims about returns and retirement outcomes."
Others are frustrated with the likelihood of the bill passing in its entirety.
The capital gains tax would damage business investment, Australian Chamber of Commerce and Industry chief executive Andrew McKellar said.
The changes have been heavily amended since they were first announced to give some exemptions to small business, but Mr McKellar said they would not be enough.
"Last week's concessions on the changes were an attempt by government to ameliorate some of the damage to the business community, but significant unresolved issues remain," he said.
Pauline Hanson's popularity has surged in polls and the One Nation leader used her maiden speech at the National Press Club last week to tout her party's stance on intergenerational equity and cost of living.
On Tuesday, she told the Senate carve outs to the controversial tax changes proved the policy was "fundamentally flawed".
"Capital gains tax discounts and negative gearing provide the housing so desperately needed by millions of Australians," she said, directly opposing the Greens requests Labor has agreed to.
Recent Australian Taxation Office data showed self-managed super funds held about $75 billion in assets under LRBAs, supported by $28.9 billion in debt.
Australian Finance Industry Association head Diane Tate said the arrangements were used by Australians seeking to "sensibly diversify their assets" and did not need further government oversight.
The Greens were also successful in postponing the passage of sweeping NDIS reforms by two months, which disability advocates say will give them welcome time to push for less cuts.
A now-stalled inquiry report was due on Tuesday.
The government did not yield to a third Greens' request of the softening of tax provisions that exempt existing properties from changes to negative gearing.
"The changes we have secured means that there will be fewer wealthy property investors turning up to auctions and outbidding renters who want to buy their first home," Greens treasury spokesman Nick McKim said on Tuesday.
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