Monday's vote is a major push on an issue that had stalled in the Senate and House despite overwhelming numbers of lawmakers in support in the Republican-dominated Legislature.
Sen. Jeff Wentworth, R-San Antonio, had been unable to muster the votes he needed under Senate rules to pass the issue as its own bill. After several failed attempts, Monday's vote tacked the measure onto a universities spending bill.
Supporters call it a critical self-defense measure and gun rights issue. Opponents worry concealed handguns could lead to more campus violence and suicide.
The measure has met stiff resistance from higher education officials, notably from within the University of Texas system.
