Mr Yousaf defeated rivals Kate Forbes (Skye, Lochaber and Badenoch) and Ash Regan (Edinburgh Eastern) in a leadership contest that exposed deep divisions within the party.
After Ms Regan was eliminated in the first round, Mr Yousaf defeated Ms Forbes by 52% to 48% in the second round, with Mr Yousaf receiving 26,032 votes and Ms Forbes 23,890.
The 37-year-old, the first Muslim to lead a major UK party, is set to be confirmed as the first ethnic minority leader of a devolved government on Tuesday March 28. Mr Yousaf is currently Scotland's health secretary, and was widely assumed to be Ms Sturgeon's preferred successor.
Speaking after the result was announced at Murrayfield Stadium in Edinburgh, Ms Yousaf said it was the "the greatest honour and privilege of my life" to be the next first minister, should parliament decide to elect him.
And he called on the party to unite behind him after what has often been a fractious leadership contest.
He said independence would be won "on the doorsteps" and pledged to kickstart a grassroots campaign, adding: "We will be the generation to win independence for Scotland."
Mr Yousaf added: "In the SNP we are a family. Over the last five weeks we may have been competitors or supporters of different candidates.
"We are no longer team Humza, or team Ash, or team Kate, we are one team."
Kate Forbes congratulated her colleague Humza Yousaf after he was elected as the new SNP leader. Ms Forbes said: “I issue my warmest congratulations to Humza.
“I’ve been proud to share a platform with both him and Ash over the last five weeks, and I know we will continue to work together, to make the lives of all of Scotland’s people better on the next stage of our journey to independence.
“Whatever the robust disagreements or frank exchanges of the last few weeks, I am confident we will unite behind Humza as our new party leader in the shared and common objective of independence.
“Uniformity is not unity – we can debate and disagree well, and then work together. To end poverty. To speak up for the marginalised. To create better jobs. To serve our people. I wish Humza well as he does just that.”
Later, Ash Regan said: "Congratulations to new SNP Leader Humza Yousaf. It was a lively contest, I wish him well and I back him as he leads our party - and I would encourage everyone to get behind Team SNP."
A meeting of the Scottish Greens Party Council unanimously voted for the party’s MSPs to support Humza Yousaf in becoming first minister and to continue with the Bute House Agreement - a cooperation agreement between the Greens and the SNP, which formed a minority government following the May 2021 election.
Following Mr Yousaf’s election as SNP leader, Scottish Green Co-leader Patrick Harvie MSP said: “We congratulate Humza Yousaf on his election and look forward to building on the successes of the last 18 months."
Quick to welcome Mr Yousaf's victory was an early supporter of his, Na h-Eileanan an Iar SNP MSP Alasdair Allan. “I am delighted to welcome Humza as the new leader of the SNP and next First Minister of Scotland," Dr Allan said. "His election is a momentous occasion for our party and for Scotland as a whole.
“Humza is an exceptional politician with a proven track record of service to the people of Scotland. His passion, intelligence and dedication will be invaluable as we work to build a brighter future for our nation.
“As a leader, he will bring a fresh perspective to the SNP, and I am confident that he will work tirelessly to strengthen our party and deliver positive change for Scotland. His vision for an independent Scotland is one that resonates with people across the country, and I am excited to see what he will achieve in the years ahead.”
Another cheerleader for Mr Yousaf, Argyll and Bute's SNP MSP Jenni Minto, said: "Congratulations to the new SNP leader and the next First Minister of Scotland Humza Yousaf."
Angus Brendan MacNeil, SNP MP for Na h-Eileanan an Iar, said: "Congratulations to Humza Yousaff on being elected as SNP leader and well done to Kate Forbes and Ash Regan for taking part. 4 months, last Thursday, since the Supreme Court - hopefully now the resultant promised Special Conference will happen."
The former SNP leader at Westminster, the Ross, Skye and Lochaber MP Ian Blackford, added: "Congratulations to Humza Yousaf on being elected leader of the SNP this afternoon. I am delighted that Humza has been elected our leader and will become our First Minister. Humza has what it takes to lead the SNP and Scotland. He will govern well and complete Scotland's journey to independence."
Scottish Labour leader Anas Sarwar also extended his "sincere congratulations to Humza Yousaf on his election.
“While I question his mandate and the SNP’s record, it is important to reflect on the election of what will be the first First Minister from an ethnic minority background. Regardless of your politics, this is a significant moment for Scotland.
“But while Scotland faces the twin crises of the cost of living and the NHS emergency, it is clear that the SNP does not have the answers that Scotland needs.
“This chaotic and divided party is out of touch and out of ideas.
“Humza Yousaf has inherited the SNP’s woeful record, but he has not inherited Nicola Sturgeon’s mandate.
“We need an election now, and Scottish Labour is the change that Scotland needs.”
The Conservative MSP for the Highlands and Islands, Jamie Halcro Johnston, said: "While the SNP’s turbulent leadership contest may have ended, choosing the SNP HQ-backed continuity candidate, Humza Yousaf, will leave the party more divided than ever.
“Under Nicola Sturgeon's leadership, Scotland was plagued by division, failed policies, and an obsession with independence at the expense of delivering better public services and a strong economy. The election of her favoured candidate will do nothing to change that.
“Humza Yousaf has been part of an SNP administration during a time of decline in Scotland’s education, healthcare, and infrastructure. Many Scots will be rightly concerned about what SNP members now giving him the keys to Bute House will mean for the future of our country.
“For those of us in the Highlands and Islands, the election of another Central Belt nationalist politician with little understanding of, and no interest in, our region is extremely worrying.
“Local people will remember his failed tenure as Transport Minister and the promises he made but didn’t deliver. And his time as Health Secretary has seen too many local health services either reduced or cut entirely, and longer waiting lists for local patients.
"Humza Yousaf has already promised to continue the SNP's obsession with independence which comes at the expense of the real priorities of the Scottish people.
"Scotland needs real change, and the SNP has failed to deliver that change. They offer only more of the same narrow nationalism with Humza Yousaf, and Scotland will be the worse for it."
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