The law, which affects 50 state institutions, was opposed by both the State Board of Regents and the University of Tennessee system.
Gun control on college campuses is a growing focus in the national debate over access to guns.
Including Tennessee, 10 states now allow guns on campus, although the Tennessee and Arkansas laws allow only faculty and staff to carry handguns, according to the National Conference of State Legislatures, which tracks policies in all 50 states.
In Georgia, Governor Nathan Deal, a Republican, is expected on Tuesday to either sign or veto a measure that would allow licensed gun owners ages 21 and over to carry concealed handguns on the campuses of public colleges and universities in that state.
On Aug. 1, 2016, a so-called campus carry law takes effect in Texas, allowing people 21 and older with a concealed handgun license to carry handguns in classrooms and buildings throughout the University of Texas system.
In Tennessee, anyone carrying a gun under the new law must have a permit and notify local police or campus security, whichever has responsibility for law enforcement on campus.
Students are not allowed to carry handguns on campus.
The law does not allow handguns to be carried into arenas and stadiums during school-sponsored events, and guns are barred in meetings related to disciplinary or tenure matters.
Haslam had said he did not believe the state should get involved in such local matters, but chose not to veto the bill.
“Although SB 2376 does not go as far as I would like in retaining campus control, the final version of the bill included input from higher education and was shaped to accommodate some of their concerns,” he said in a Monday statement.
Proponents said the bill will lead to greater safety on campuses. Opponents voiced concern about the safety of students, faculty and visitors on campus.