He is taking over from Nicola Sturgeon, the country’s longest-serving leader, who revealed she was stepping down in a surprise announcement last month.
And with Deputy First Minister John Swinney stepping down alongside Ms Sturgeon, sweeping changes are inevitable.
These are the most pressing issues facing the new leader.
Independence is the party’s raison d’etre but progress on the cause has stalled in recent years, despite the ruling Scottish National Party’s grip remaining strong in the UK Parliament among voters in Scotland.
Ms Sturgeon said she believed the cause of gaining independence for Scotland would be better served with someone new leading the SNP.
The country voted against the independence in 2014.
Polls show little public appetite for another referendum, with a majority disagreeing with the case for Scotland to go on its own.
There is also the question over how the new leader can take the argument for a second referendum forward legally.
Ms Sturgeon had hoped to hold another poll this October on the question of whether the country should break away from the UK.
But in November the UK's highest court ruled that the Scottish Government could not force a second referendum on independence without Westminster's consent — something UK Prime Minister Rishi Sunak is not prepared to give.
In response Ms Sturgeon said the SNP would use the next UK general election as an attempt to show a majority of people in Scotland support independence.
But whether a new leader will successfully reignite that desire — legally, in terms of a second referendum, and among voters — remains to be seen.
Pressure over health care
The record of Scotland’s Health Secretary Mr Yousaf has come under fire — leadership rival Kate Forbes and other opposition politicians branded him the worst health secretary since devolution, with NHS waiting times growing and delayed discharges increasing under his stewardship.
Tackling the problems faced by a health service still recovering from the pandemic will certainly be high on the to-do list for Scotland’s new leader.
Mr Yousaf has claimed success in preventing strike action by NHS workers north of the border to date but junior doctors in Scotland are to be balloted on industrial action in a vote which starts on Wednesday, meaning talks with their representatives will have to be another priority.
Shoring up the coalition
It could be key to keeping the SNP’s power-sharing agreement with the Scottish Greens intact.
The Bute House Agreement between the two parties brought Green politicians into government for the first time anywhere in the UK — and crucially gives the SNP a majority in Holyrood.
The Greens insist they want to maintain the “progressive” policies pursued by Ms Sturgeon.
Rebuilding a party rocked by division
The SNP has lost about 30,000 members in little more than a year.
The mishandling of the situation — with the party initially having rubbished reports its membership had fallen by such a margin — led to the resignations of SNP communications chief Murray Foote and long-standing chief executive Peter Murrell, Ms Sturgeon’s husband.
These will be key positions for the party to fill as it prepares to fight a Westminster general election, which will likely take place next year.
Working with Westminster
Alistair Jack, the Scottish Secretary, has said Holyrood ministers have “too often” sought conflict with Westminster, “simply to further their goal of separation”.
“That has sapped the energy, focus and resolve, which should have been directed at improving education, tackling drugs deaths and ensuring people have the reliable transport links they need,” he said.
“Whoever wins the leadership election faces a fundamental choice, which will define their time as First Minister.
“It is fair to say that they and I will have fundamental political differences.
“But this should not, must not, be an obstacle to us working together in the interests of Scottish families and businesses.”
He continued: “After eight years of Nicola Sturgeon’s leadership, whoever wins has the chance to seize an opportunity to do things differently, to reset and to make devolution work better for the people we serve.”