In what was a widely expected move, Mr Bandt signed an agreement with Prime Minister Julia Gillard in her Parliament House office this morning.
They were joined by Deputy Prime Minister Wayne Swan, Greens leader Bob Brown and his deputy Christine Milne.
It moves Labor's tally to 73 seats.
In return for Mr Bandt's support, Ms Gillard has offered to set up a climate change committee, make investments in dental care as well as $A20 million to look at high-speed rail on the east coast.
There will also be a parliamentary debate on Afghanistan and restrictions placed on political donations.
The government had also agreed to move towards holding a referendum to change the constitution to recognise indigenous people and local government, Senator Brown said.
The climate change committee, operating at cabinet level, would move towards setting a price on carbon.
He said this all remained a work in progress.
"I spoke with Mr Abbott last night," he said. "He told me that he would attack any agreement that we signed up on.
"I said that's his right.
"I reminded him that he may well be the prime minister next week although we favour Julia Gillard leading the next government of Australia and are working to that end quite clearly.
"We have made a decision here.
"We are the first people in this balance of power in both houses to make a decision. We think that will help lead to others making a decision."
Senator Brown said if Mr Abbott became prime minister, he would then meet him to work out processes for how the Senate would work.
"I give a commitment here to whichever is the next government - our job is to provide the best Senate accountability for that government and we will do just that."
Senator Brown told reporters the Greens were happy with the agreement they'd negotiated.
The climate change committee, to be made up of parliamentarians, "will look at all the options available to achieving a carbon price", he said, which was a key priority for the Greens.
"We've got this agreement, we're happy with it."
But asked if it meant Ms Gillard would then need to scrap her citizens assembly on climate change, Senator Brown said reporters would have to ask her.
The negotiations were a good example of how parties could work together on a consensus basis, which was what the Australian people were demanding, he said.
He also defended a lack of progress on some issues, including allowing a conscious vote on same-sex marriage.
"We didn't reach an agreement on that matter."
Senator Milne said European nations used the process of a parliamentary committee representing all interests committed to a certain idea and including subject matter experts.
She said the idea was to come up with a parliamentary consensus supported by everyone.
"The proviso for membership of the committee is that the people going onto it are committed to a carbon price," she said.
"They may not all agree with the mechanism of achieving a carbon price."
Senator Brown said he had first put the idea of the climate change committee to Ms Gillard some days ago, and in a "happy conjunction" she had put the same idea on the table.
He would not put "pre-conditions" on the deal such as securing a carbon price within the next three years.
The Greens would also contribute to the budget process, Senator Brown said.
"We will be able to feed ideas into the budget process," he said. "The budget ultimately will be shaped by the government."
He and Mr Bandt would meet with Ms Gillard or her representative every week in sitting periods and once a fortnight in other periods to work on the legislative agenda.
The agreement did not apply to the Greens' relationship with a Labor opposition.
