Gov. Bill Haslam and Nashville Mayor Karl Dean announced the program at a press conference on Monday.
The public-private partnership is an expansion of a larger initiative that provides scholarships to students in 26 other Tennessee counties.
Officials say the program helps students who may not be able to pay tuition but want to further their education at a community or technical institution.
So far, supporters have raised $1 million to launch the program in all 20 Nashville high schools, and the city is proposing up to $750,000 for the program over the next two years. The program also has a component that provides mentors for students.
Haslam said the program ties in with his "Drive to 55" initiative that's intended to increase the number of Tennesseans with at least a two-year college degree or certificate.
Currently, 32 percent of Tennesseans have a two-year degree or higher, and Haslam's goal is to raise that number to 55 percent by 2025.
The governor said the new education initiative in Nashville will also help attract businesses to the Music City.
"There's a synergy to it," he told reporters after the press conference. "The better graduates we produce, then the more businesses are going to say we want to be here."