From The Dallas Morning News:

Under the measure by Sen. Craig Estes, R-Wichita Falls, Texas would join most other states in authorizing open carry of handguns — as long as the person has a state concealed handgun license. Currently, about 826,000 Texans have concealed handgun licenses, nearly 3 percent of the state’s population.

The bill, approved on a party-line 20-11 vote, would be effective on Jan. 1, 2016. Texans can already carry long guns, such as rifles, openly.