Education Secretary Mike Russell said the Scottish Government has set aside £4 million to pay for the scheme, which will run for just over 10 weeks.
Up to 4,000 employers in businesses of all sizes and all sectors should be able to benefit.
Mr Russell announced details of the latest initiative to boost apprenticeships ahead of a jobs summit in Glasgow today.
And he stressed that apprentices were "vital for Scotland`s recovery".
The Education Secretary said: "Today I want to offer all businesses across Scotland £1,000 to take on a new apprentice.
"This will benefit our hard working companies and employers who continue to fight the effects of the recession. It will also provide increased skills training opportunities to thousands of individuals across Scotland."
He went on: "No sector has been immune from the recession and people of all ages are being affected. That is why today`s incentive is being broadened out to cover all sectors and apprentices of all ages."
And he said: "The action we are taking shows that we are doing everything we can to make sure that businesses continue to invest in training for the people who will be our workforce of the future."
Skills Development Scotland is taking a leading role in working to support apprenticeships.
Damien Yeates, the chief executive of the national skills body, said: "For many years businesses have benefited from motivated and capable trainees and it's very encouraging that yet more people and organisations will be able to make use of the scheme through the new Modern Apprenticeships Grant, launched today."
The grant scheme will run from today until March 26.
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