ITV News Correspondent Peter Smith has more details on the deal
This announcement has come as the two parties have agreed a power sharing deal for the duration of the current Scottish Parliament term.
In a statement of priorities entitled 'Working Together to Build a Greener, Fairer, Independent Scotland' the parties state they will "secure a referendum on Scottish independence after the Covid crisis. This would be within the current parliamentary session on a specific date to be determined by the Scottish Parliament. If the Covid crisis has passed, our intention is for the referendum to be within the first half of the five-year parliamentary session".
In the 2014 referendum, the Scottish Borders voted against independence by 66.56 per cent to 33.44 per cent in favour. In Dumfries and Galloway, the numbers were 65.67 per cent and per cent respectively.
Two Green MSPs will become Scottish Government ministers under the new confidence and supply agreement.
The agreement, which has been negotiated over a number of months, will cement the pro-independence majority in Holyrood.
A document published on the Scottish Government website today said two Green MSPs will be nominated to become ministers - the first time the party has taken such a role in the UK.
Under the terms of the deal, Green MSPs would support the Scottish Government on confidence votes, as well as in annual budgets if there is "appropriate funding for the shared policy programme".
A number of areas are excluded from the agreement though, including much of aviation policy, the future of green ports, and direct financial support to businesses involved in the aerospace, defence and security sectors, field sports and the economic principles related to concepts of sustainable growth and inclusive growth.<
The PA news agency has said it understands a meeting of the Scottish Cabinet approved the power sharing deal this morning.
The two parties have been locked in negotiations since May, after the SNP fell one seat short of an overall majority at the Holyrood election.
The agreement stops short of a formal coalition between the two but they pledge to work together on key issues, including on a Scottish independence referendum after the coronavirus pandemic.
Scottish Tory net-zero spokesman Liam Kerr said the Green manifesto from May's election was a "doctrine to start a war on working Scotland", after it proposed a move away from North Sea oil and gas, and the end of new road-building projects.
Scottish Labour leader Anas Sarwar has challenged the Greens to stand against further cuts to council budgets.
He said: "If the Greens are to be anything more than simply the SNP's lackeys, they need to rediscover their principles and fight for a greener Scotland rather than roll over to the SNP every time the going gets tough."
A spokesman for the Scottish Greens said: "It's no surprise that parties only interested in scoring political points would be alarmed about any suggestion of co-operation in the interests of people and planet.
"People vote Green to get results, and over the last five years the Scottish Greens have achieved more from our manifesto than Labour and the Tories combined. We will continue to do that, whatever happens."
A spokesman for the First Minister said: "Following the SNP's record landslide election win in May, the First Minister extended an open invitation to all parties to discuss areas where they thought they could work closely with the SNP in Government for the common good - in the face of the extraordinary challenges facing us such as the climate emergency and recovering from the pandemic.
"The fact that Labour and the Tories chose not to pursue that offer says far more about them than anyone else."