Mr Swinney reacted on social media after the party confirmed he was the only candidate to succeed Humza Yousaf, who announced one week ago he was stepping down as SNP leader and Scottish First Minister.
Mr Swinney is now expected to go on to become Scotland’s seventh first minister, though before he does he will need to win the backing of MSPs in a vote at Holyrood.
That ballot could take place as early as Wednesday, with Mr Swinney likely to be officially in place in the top job in Scottish politics the following day.
Commenting after it was confirmed he was the only candidate, Mr Swinney posted on X, formerly known as Twitter that he was “deeply honoured to have been elected as Leader of @theSNP”.
He pledged: “I will give all that I have to serve my party and my country.”
Mr Yousaf’s tenure as first minister came to an end after he tore up the powersharing agreement the party had enjoyed with the Scottish Greens at Holyrood, which left him facing a vote of no confidence in his leadership.
That means Mr Swinney will have to lead a minority government at Holyrood, requiring support from other parties before vital legislation can proceed.
Mr Yousaf congratulated Mr Swinney as his successor as SNP leader and called on the party to heed his call for unity.
He posted on X, formerly Twitter: “Congratulations to @JohnSwinney on becoming leader of @theSNP and FM-elect.“
“John’s central message has been one of unity. As a party, we must heed his call, whatever has happened in the past should remain there.
“Let’s get behind John & his team so they can deliver for Scotland.”
It is the second time that Mr Swinney has taken on the leadership of his party, having previously held the job from 2000 to 2004.
But then he was leader of the main opposition party at Holyrood, with a Labour-Liberal Democrat coalition in charge.
Now, after holding a variety of senior posts in the Scottish Government, including finance secretary, education secretary and deputy first minister, a position he held for eight years under Nicola Sturgeon, he will get his first chance to be first minister.
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Confirmation of Mr Swinney’s appointment as party leader comes 25 years to the day after the first elections to the Scottish Parliament with Mr Swinney one of only three MSPs to have held the same seat at Holyrood continuously since then.
While Mr Yousaf’s downfall was sparked by his decision to terminate the powersharing deal the SNP had had with the Scottish Greens, the smaller pro-independence party urged Mr Swinney not to ditch the “progressive” agenda that had been enshrined as part of that arrangement.
Scottish Green co-leader Patrick Harvie said the party’s seven MSPs would meet to discuss how they would vote in the ballot for first minister.
Mr Harvie stated: “We are committed to delivering on our vision of a fairer, greener and more equal Scotland, and are open to talks with John Swinney and his team about how we can work together to make that happen.”
He added: “Scotland needs a period of stable government.
“Mr Swinney knows that if he is to have our support then it must be on the basis of progressive policies that help us to tackle the climate crisis and build a fairer and more equal future.”
The Green MSP added: “There are a lot of important policies already on their way to delivery as a result of the Bute House Agreement, including better rights for tenants and rent controls, transforming the way we heat our homes and a watertight ban on conversion therapy.
“We remain utterly committed to these policies and will oppose any move away from them or steps to dilute them.”
Scottish Conservative leader Douglas Ross meanwhile urged Mr Swinney to “govern for all of Scotland by abandoning his relentless push for independence”.
Mr Ross insisted his party would seek to “hold John Swinney to account when he lets the Scottish people down – just as we’ve done with Humza Yousaf”.
But the Conservative added: “It’s difficult to see how he can be the fresh start Scotland needs, when he’s the ultimate continuity candidate.
“John Swinney was joined at the hip with the disgraced Nicola Sturgeon and his fingerprints are all over her numerous policy failures and cover-ups.”
With Mr Swinney having led the SNP previously between 2000 and 2004, Mr Ross went on to question if a “failed former leader from two decades ago – who, as education secretary, sent Scotland plummeting down international league tables” was the best person to lead the country.
He claimed: “With John Swinney at the helm, the SNP will double down on their independence obsession, the one issue they agree on, and ignore the real priorities of the Scottish people, such as fixing our ailing public services and growing the economy.”
Meanwhile Scottish Labour leader Anas Sarwar said “John Swinney’s coronation is entirely about managing the SNP rather than running our country and delivering for Scotland.
“At a time when Scotland is crying out for change, the SNP is offering more of the same.
“John Swinney has been at the heart of this incompetent government for 17 years and at the heart of the SNP for 40 years.”
Mr Sarwar said: “From presiding over the exam results scandal as education secretary to destroying public finances as finance secretary, John Swinney’s record is one of failure.
“This is a stitch-up by a chaotic and dysfunctional party that is more interested in protecting its own interests than serving the interests of the people of Scotland.”