The funds would help develop a medical school and teaching hospital in Austin. The proposal will be on the November ballot.
Board members say now is a good time to move forward with the project because of the federal Medicaid matching funds available.
The tax proposal is the latest step in a series of developments surrounding a medical school. As KUT News previously reported, in April, Seton Healthcare Family, which currently operates University Medical Center Brackenridge, said it would spend $250 million on a new teaching hospital.
Soon afterward, the University of Texas Board of Regents proposed $30 million in annual funding for a medical school for the first eight years, and $25 million annually after that.