University President Glenda Glover says financial hardship is the main reason many students can't return.
State lawmakers approved the funds, which were included in Gov. Bill Lee's budget.
Student Government Association President Katelyn Thompson says many talented out-of-state students worry about paying tuition and fees.
The university in 2017 implemented higher admissions standards and began initiatives to improve retention and graduation rates.
Tennessee State said the funds will be received as a lump sum with the fiscal year beginning July 1.
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