Under a pledge first reported in the Daily Record, an expansion of the universal childcare programme would be rolled out in Mr Yousaf’s first Budget if he comes SNP leader.
The commitment will be one of the most significant pledges made to date in the leadership race to succeed Nicola Sturgeon.
Finance secretary Kate Forbes and former community safety minister Ash Regan are the two other candidates in the race.
Mr Yousaf said he would use his first Budget to expand free provision, with a goal of offering 22 hours a week throughout the year.
He also announced plans for a £25 million annual “helping hand fund”, which would offer parents returning to work a £500 loan towards childcare costs.
Currently, three and four-year-olds can access up to 1,140 hours of funded early learning and childcare a year, which is around 30 hours a week in term time.
Some two-year-olds are also eligible for free childcare on a means-tested basis, with around a quarter of the age cohort having this entitlement.
Mr Yousaf said: “Young families in Scotland are being hit hard by the cost-of-living crisis.
“As a parent myself, I know how hard it is for many going back to work while juggling the commitments of childcare and employment.
“For those on low incomes in particular the upfront costs of childcare, transport and higher household bills are serious financial barriers stopping many parents getting back to work – especially in those first few months after returning to work when households budgets are stretched.
“As first minister, my Helping Hand Fund would help working families by easing that burden, offering £500 loans towards the first stages of childcare to help all parents in Scotland returning from leave back into employment.
“A win-win for Scotland – cutting household costs, helping families get back into work and boosting our economy.
“We know that expanding childcare has saved families thousands of pounds every year.
“If elected as first minister I’ll go even further.
“In my first budget as Scotland’s first minister, I will accelerate the rollout of free early years education for one and two-year-olds in Scotland – offering high-quality childcare for 22 ours a week, all year round.
“I want Scotland to be the best country in the world to grow up.
“My announcement today goes some of the way to ensuring we give our youngest Scots the very best start in life.”