The First Minister set out plans to use the power to create new benefits coming to the Scottish Parliament to support those aged between 16 and 24 with the costs of going back to work.
The grant of £100, or £250 for those with children, will be offered to young people who have been out of work for six months and are starting a job for more than 16 hours a week.
Young people who are entitled to the money will also receive help for public transport costs for up to three months.
The SNP said the grant could help around 6,000 young people a year as part of a drive to reduce youth unemployment by 40% by 2021.
Ms Sturgeon said: “Under the SNP Government, youth employment has risen to its highest level since 2009 and is now the highest of any country in the UK.
“Over the next parliament we want to go further and reduce youth unemployment by 40%. The new SNP Jobs Grant will help those who have been out of work to start a new job and prevent young people slipping into long-term unemployment.
“Starting work comes with additional costs such as work clothes and travel expenses and for young people who may have no savings it can be difficult to get started.
“I want to see all our young people in work, training or employment. Over the next parliament we will increase the number of apprenticeships, bring employers, colleges and schools closer together to help young people into work, continue to support free education and support young people as they find employment.”
Earlier, Ms Sturgeon defended her decision to rule out introducing a 50p top rate of income tax when the new tax and welfare powers come into effect next year.
She has said the move would be “reckless” and “daft” in light of analysis suggesting it could lose Scotland £30 million.
Ms Sturgeon told BBC Radio Scotland’s Good Morning Scotland programme: “I’m being upfront and frank about this. I will want to look on a year-by-year basis to see if there are ways in which the Scottish Government, within the limited powers we have, can mitigate this risk but I’m also saying clearly that it would not be a sensible thing for me as First Minister to do to raise a tax knowing that it might reduce the amount of revenue I’ve got to spend.”
She was pressed to set out whether the SNP’s named person scheme - under which every child under 18 is assigned a single point of contact, such as a teacher or health visitor, to look out for their welfare - is mandatory or voluntary.
Ms Sturgeon said: “Every young person will have a named person but no parent is required to pay any attention to what a named person says if they don’t want to do that.
“It is a universal service, a universal entitlement. The reason for that is to try to avoid vulnerable young people or young people who are at risk for whatever reason falling through the net.”