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By Mary McCool
BBC Scotland news
John Swinney will be sworn in as the seventh first minister of Scotland later.
He is then expected to form his government, with cabinet posts confirmed in parliament on Thursday.
A "significant" role has been promised to former finance secretary, Kate Forbes, who chose not to run for the SNP leadership and backed Mr Swinney.
Overall he was backed by 64 MSPs and seven Green MSPs abstained, guaranteeing him the required majority.
Mr Swinney's appointment as first minister will be rubber-stamped by the King before he is officially sworn in at the Court of Session.
Following a tumultuous two weeks for the SNP, Mr Swinney became party leader on Monday.
A contest was narrowly avoided, with a rival candidate - veteran SNP activist Graeme McCormick - withdrawing his bid at the 11th hour.
This paved the way for Humza Yousaf to formally resign as first minister on Tuesday - a move prompted by his tearing up of the power-sharing agreement with the Scottish Greens.
He had been in post for just over a year, having taken over the role from Nicola Sturgeon.
Mr Swinney has 16 years' cabinet experience and led the SNP between 2000 and 2004.
He will take office in the week the Scottish Parliament marks 25 years since devolution.
Previously, he said he would not be an "interim leader" or a "caretaker" and that he intended to see out a full term.
He has said he will seek to govern on a "moderate centre left" platform, and will be open to working with any other political party in the parliament to pass legislation.
This was reflected in his speech to MSPs on Tuesday in which he struck a conciliatory note, praising the achievements of other major parties in the devolved parliament.
He pledged to be the "first minister for everyone in Scotland", adding: "I am here to serve you, I will give everything I have to build the best future for our country."
The economy, the NHS and other public services, and "a drive to lift children out of poverty" are his priorities for government.
Kate Forbes is expected to make a return to cabinet but it is unclear where other ministerial roles will be allocated.
It is also not clear which roles Mr Swinney will keep, though The Times previously reported he intended to have a "slimmed-down" government.
Having confirmed he has no intention of resurrecting a deal with the Greens, Mr Swinney will attempt to pass a budget and other key bills with a minority administration of 63 MSPs.
Until recently Mr Swinney's career on the frontbenches looked to be over.
He stepped down from the cabinet in 2023 after 16 years in key roles under both Alex Salmond and Nicola Sturgeon.
Following the collapse of the Bute House Agreement, and Mr Yousaf's resignation, Mr Swinney was publicly urged to stand for first minister by senior party members - which he said he accepted out of a "profound sense of duty".
The SNP leader said the decision had been made with his family, expressing "eternal gratitude" to his wife Elizabeth Quigley, who has multiple sclerosis and relies on him for support.