The places are intended to provide educational qualifications and workplace training for senior school pupils and potential graduates.
They are in addition to the modern apprentice programme, which supported more than 26,000 people last year.
Skills Development Scotland said work-based learning was vital for Scotland’s future prosperity.
Jobs agency SDS said it was supporting 2,600 foundation apprenticeships for pupils and more than 900 graduate apprenticeships in 2018.
The programme are backed by employers, universities, colleges and schools across the country.
The foundation scheme aims to give work skills training for fifth and sixth year school pupils alongside academic qualifications such as Highers.
The graduate scheme does the same for older entrants studying up to masters level.
Diane Greenlees, head of foundation and graduate apprenticeships at Skills Development Scotland, said apprenticeships were essential for the Scottish economy.
“Over the next 10 years we are facing significant and rapid technological change across all our growth sectors, along with global competition,” she said.
“Young people now need to have a different set of skills and qualifications to help them succeed in the workplace.