This measure has long been sought after by conservative gun owners, despite previous objections from law enforcement and gun control groups about the risk this new legislation could pose to the public.
The Republican-led legislature approved the measure on Monday, sending the bill to the Republican governor’s office for signature.
Mr Abbott has already indicated that he will sign the bill once he reaches his office.
“We should have a ‘constitutional deferral’ in Texas,” Abbott told North Texas radio host Rick Roberts in April.
Current Texas law requires gun owners to be permitted to carry a handgun, both concealed and open. Applicants must also submit their fingerprints, complete four to six hours of training, pass a written exam, and then pass a marksmanship test.
But Texans are already allowed to openly carry a rifle without a license.
The new law, if signed by Mr Abbott, would be similar to what it is for rifles by allowing gun owners to openly carry a handgun without going through licensing, verification requirements background or other training.
Businesses would still be allowed to prevent people from carrying guns in their establishments under the new bill. Federal law requiring a background check when purchasing specific firearms would also apply despite this new law in Texas.
Texas already has some of the easiest gun laws in the United States for its more than 1.6 million handgun license holders.
But that hasn’t stopped gun owners from pushing harder for legislation that would make gun ownership and carrying more accessible.
The Senate made several changes to the House bill before it was passed to allay some concerns of law enforcement groups. This included removing an amendment that would have prevented police officers from questioning someone based solely on their possession of a handgun.
But gun control advocates have expressed concern over the passage of this bill given the increase in mass shootings in Texas in recent years, such as the El Paso Walmart shooting and the Sutherland Springs Church shootout.
Representative Joe Moody, a Democrat from El Paso, expressed his disapproval to lawmakers over the bill after the state legislature did nothing to change gun laws as a result of the mass shooting at Walmart, which left 23 dead and 23 injured.
” All [El Paso community members] wanted was something better. All they wanted was some responsibility. Yet here we are, ”Mr. Moody said on Sunday. Texas Tribune reports. “When the doors were closed, I heard a lot of promises. I haven’t heard them since.
However, supporters of the legislation stressed that the mass shootings did not involve handguns.