Finance secretary Kate Forbes announced the deal with the Greens while giving evidence to the finance and constitution committee on Monday.
And Scottish Lib Dems leader Willie Rennie later confirmed his party would also back the budget in exchange for more than £300 million in support for mental health, education and councils.
The Greens have helped push through each of the Scottish Government’s five budgets in this parliamentary term, every time extracting concessions from the finance secretary.
Last year, the main ask of the party was free concessionary bus travel for young people, which Ms Forbes agreed to extend to those under 22 years old in this round of negotiations.
Greens co-leader Patrick Harvie said he was “delighted” his party’s “constructive approach” had again yielded results.
In return for their support, Ms Forbes has agreed to pay rises for public sector workers, amounting to £800, or around 4 per cent, for those earning under £25,000, 2 per cent for those between £25,000 and £49,000 and 1 per cent above that.
The Greens also secured Covid-19 relief payments of up to £130 for low-income families as well as two further instalments of £100 each in August and December for families with children eligible for free school meals.
Half a million families will receive the smaller payment, while 170,000 will be eligible for the full £330, the Greens have said.
All primary school pupils in Scotland will also be able to claim free school meals during term time, under the new plans, and £40 million will be invested in active travel, energy efficiency and other environmental efforts.
Ms Forbes said: “I’ll be able to say more at stage three, but I wanted to take the opportunity to update the committee transparently on this recent development.”
Mr Harvie said: “I’m delighted that once again our constructive approach has delivered real results for the people who need it most.
“The Covid household relief payment will direct money to those households who have struggled in this crisis, providing funding for essential supplies.”
He added: “This year’s budget cements the impact the Scottish Greens have had on Scotland’s priorities over the last five years.
“From fairer taxes to local services, we’ve shown every year that Green MSPs will get things done.”
The Scottish Lib Dems separately secured a range of budget concessions, including an extra £120m for mental health services as well as a further £60m for smaller class sizes.
An extra £20m will provide more in-class support to children who need it by topping up the Pupil Equity Fund, while £15m has been agreed in special allocations to the North East to pay for skills training.
Mr Rennie said: “We think that people expect parties to work together in the middle of a pandemic. Our focus has been to put recovery first.
"We have highlighted the need for business support, an education bounce back plan, and better mental health services, given the pressure we know that the virus crisis has put on people.”
Scottish Labour will also back the budget if it includes an increase in social care workers’ pay to £12 per hour, rising to £15 in the next Parliament.
The party said the median hourly wage for UK care workers is £9.50 and a pay rise would benefit as many as 200,000 people in Scotland.
Speaking to journalists on Monday, Mr Sarwar said a deal with his party would have cost more than the Greens.
He said: “It’s not a case of Labour being on the sidelines, it’s the opposite in fact.
“Jackie Baillie has been in active negotiations with Kate Forbes at before stage one, at stage one, before stage two, at stage two and as we head into stage three.
“Those negotiations were actually working fairly positively from my understanding from Jackie.”