The Scottish Government hopes the move will reach beyond the current crop of graduates to address the shortage of teachers in some parts of the country.
Recent months have seen Trinity Academy in Edinburgh and Blairgowrie High School in Perthshire appeal to parents for help in finding maths teachers.
The government has also come under fire over falling literacy and numeracy standards in Scotland’s schools during its decade in power.
First Minister Nicola Sturgeon’s recent Programme for Government was built around the creation of a high-tech, skilled economy, but there are concerns over the number of teachers in key technical subjects.
Now bursaries of £20,000 are to be created for workers wishing to change career and become a teacher in priority science, technology, engineering or maths (STEM) subjects. The plan was unveiled as Mr Swinney addressed delegates at the SNP conference in Glasgow yesterday.
The Scottish Government expects up to 100 people a year could apply for the bursaries – meaning annual costs of £1 million.
“In schools in some parts of our country and in some subjects we know we have a shortage of teachers,” Mr Swinney said. “We have taken a range of actions to help councils tackle that problem and now I want to go further.
“STEM subjects – science, technology, engineering and maths - are crucial, not just to the education of our children but the future of our economy.
“We need to recruit more teachers in these subjects. And to do that, we need to reach beyond recent graduates and attract people who have the appropriate subject degree but are working in business or industry.”
School subjects which will be eligible for the bursaries are maths, computing science, physics and technical education but these will be reviewed each year according to need.
These “career-changers” still need to go through initial teacher education before they can become teachers.
Mr Swinney added: “We understand that they have to balance family and financial responsibilities that new graduates may not face, we understand that the prospect of giving up a salary for a year while they do their teacher training is a real barrier for them.”
Mr Swinney – who is also the Education Secretary – insisted the system was fundamentally strong despite a recent fall in global league tables for standards in reading, writing and maths.
The Programme for International Student Assessment (PISA) for 2015 found Scotland has tumbled down league tables for maths, reading and science when compared to 34 other developed countries and the UK’s three other home nations.
Record low scores mean it no longer performs above the international average in any of the three core subject areas and the number of countries performing better than Scotland has increased in each report conducted since 2006, the year before the SNP came to office.
Overall, Scotland’s ranking has dropped from 11th to 23rd for reading since 2006, from 11th to 24th for maths and from 10th to 19 for science.
The SNP has also faced criticism over a fall of about 4,000 teachers in Scotland’s classrooms since the party came to power in 2007.
But Mr Swinney’s defended the education system yesterday.
He said: “We will have no truck with the deliberate misrepresentation of Scottish education put forward by our opponents.”
“There are challenges – not least around literacy and numeracy – but Scotland has a fundamentally strong education system.
“We are committed to reform - not because we share our opponents demoralising view - but because we want our schools to be even better.”
And he pledged to press ahead with education reforms which will see head teachers in schools handed greater autonomy over what is taught in their classroom has part of a plan to drive up standards.
The reforms, which follow a review of school governance, will also give parents a stronger voice in the running of schools and were backed after a vote by MSPs at Holyrood earlier this year.
But the bursary announcement met with short shrift from opponents yesterday.
Tory leader Ruth Davidson claimed the idea was in their party’s 2016 Holyrood manifesto and even tweeted a picture of the section of the document.
“I thought that post graduate teaching bursary idea was a good one. When we wrote it. In our 2016 manifesto,” Ms Davidson said
Labour education spokesperson Iain Gray added: “Hardly a day goes by now without the SNP U-turning and giving in to Labour demands.
“Scotland’s schools are blighted with a teaching shortage, with 4,000 fewer teachers since the SNP came to power, and urgent action is needed.”
“We welcome John Swinney adopting one of the policies from our ten point plan for Scotland’s schools, and look forward to him seeing the sense of the other nine too.”
The Deputy First Minister hailed Ms Sturgeon’s recent legislative programme for the coming year as being “easily the most ambitious programme of any government since devolution”.
And he made a fresh rallying call to party member for Scotland to break away from the UK.
“We rededicate ourselves to independence – the best possible future for Scotland,” Mr Swinney added.