Mr Yousaf defeated rivals Kate Forbes and Ash Regan in a leadership contest that exposed deep divisions within the party.
The 37-year-old is the first Muslim to lead a major UK party.
Mr Yousaf is currently Scotland's health secretary and was widely assumed to be Ms Sturgeon's preferred successor, although she did not explicitly back any of the candidates in the contest.
The leadership election was decided by the Single Transferable Vote system, with 50,490 of the SNP's 72,169 members casting a ballot - the vast majority of them online.
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 new SNP leader will face a vote in the Scottish Parliament - which he is virtually certain to win - on Tuesday before becoming Scotland's sixth first minister.
A historic day however you look at it, and whoever you backed in the leadership contest. We now have a leader of Scottish Labour, an SNP leader and a UK prime minister who are all from Asian backgrounds (for better or worse in some cases).
As it happens, Yousaf got my first preference, and Forbes my second. I didn't allocate a preference to Regan, for a variety of reasons.
It wasn't an easy choice between Yousaf and Forbes. Both have their strengths and some decided weaknesses. A couple of considerations tipped it for me.
Yousaf gained far more endorsements from SNP MSPs and MPs - many of whose opinions I respect - and that probably signals the possibility of more unity among the members of both parliaments, if not necessarily among SNP members as a whole. Portrayed as "the continuity candidate", I was pleased to see him defend the SNP government's achievements in its time in office.
The fact that Forbes chose to trash some of that record during the course of the hustings counted against her. It's one thing to be healthily critical of party policies and achievements, it's quite another to parrot some of the tired claims of unionists and the bulk of the media. On a similar consideration, I didn't appreciate Forbes's tendency to rewrite the party's manifesto on the hoof and sound unsettlingly like she might try to pull the party to the right on some issues, both social and economic. She's very self-assured as a media presence and undoubtedly talented, and I hope future cabinets manage to harness her abilities and her appeal in certain quarters - one of her self-proclaimed selling points was that she had higher ratings than Yousaf among the electorate at large, though whether that means they'd actually vote for the SNP is quite another question.
There remains the vote in the Scottish Parliament on who should take over from Nicola Sturgeon as First Minister when she formally resigns. The Opposition will no doubt put up its own candidates as a formality, but with the backing of the Scottish Greens and no doubt the vast majority if not all of his own party, the job looks like Yousaf's.
That's his pen name, his real one is Paul Millicheap.
He wrote "Refugees" in 2016. Here's an extended BBC profile of him from that year: 'How I accidentally became a poet through Twitter'
Here's another of his:
Here's his website: https://brianbilston.com/
And here's his Twitter feed: https://twitter.com/brian_bilston
I've given his collections You Took the Last Bus Home, Diary of a Somebody and Alexa, what is there to know about love? to my serious poetry buff wife on successive Christmases, and she's loved them.
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