The move comes a week after the First Minister pledged close the schooling gap between rich and poor areas of Scotland and urged voters to judge her on this.
The changes unveiled by Ms Sturgeon mean school and college students will qualify for an educational maintenance allowance (EMA) even if they are earning up to £24,421 - an increase of £4,070 on the previous level.
For a family with more than one dependent child, the increase is £4,481, up to £26,884.
Students studying part-time college courses are also now eligible.
The First Minister made the announcement at Oban High School as part of the Scottish Cabinet’s visit to the town.
She said: “The Scottish Government is committed to helping families on the lowest incomes and ensuring that background and income does not hamper the prospects of our young people.
“EMAs have already helped thousands of young women and men in Scotland stay on in education to build up their skills and employability.
“From January, an additional 22,000 16 to 19-year-olds will be eligible for the weekly grant, which is in stark contrast to the Westminster government who removed EMAs from England a number of years ago.
“We remain committed to the continued availability of EMAs in Scotland to help even more school pupils and college students continue their studies and fulfil their potential.” The Government estimates that an additional 10,000 school pupils and 12,000 more college students will be able to take up an EMA after the changes take effect.
Latest figures show that grants were provided to 34,955 school and college students in Scotland in 2013-14.
EMAs were axed south of the border in 2011 by the coalition’s then-education secretary Michael Gove. The Scots-born MP replaced it with a bursary scheme which was targeted at helping the “most vulnerable” teenagers to get ahead.
UK Labour leadership frontrunner Jeremy Corbyn has pledged to reintroduce EMAs in England if he wins the contest next month.
The EMA scheme provides an incentive for young people aged 16-19 from low-income families to stay on in post-16 education, either in school or college.
The incentive is an entitlement and demand-led programme which is administered by local authorities and colleges on behalf of Scottish ministers. A weekly payment of £30 is made to a young person and is subject to attendance and agreement of a learning plan.
The new Labour leader has sought to make the gap in attainment between rich and poor areas of Scotland a key issue of her party leadership.
Scottish Labour’s opportunity spokesman Iain Gray welcomed the announcement but said “experts have pointed out that the SNP government cut the EMA budget by an estimated £11 million, so today’s announcement is largely just restoring a cut they had made themselves.”
Scottish Liberal Democrat education spokesman Liam McArthur said: “With 140,000 part-time college places axed by the SNP in recent years, it seems they have robbed Peter to pay Paul.”