The law applies to U.S. citizens 21 and older.
The new law goes into effect 90 days after the Legislature adjourns, which could happen in the next couple of weeks, The Arizona Republic reports. It is already legal to carry a firearm openly in Arizona.
Arizona joined Alaska and Vermont in permitting concealed weapons without a permit.
"I believe strongly in the individual rights and responsibilities of a free society, and as governor I have pledged a solemn and important oath to protect and defend the Constitution," Gov. Jan Brewer, a Republican said in a written statement. "I believe this legislation not only protects the Second Amendment rights of Arizona citizens, but restores those rights as well."
Former Democratic Gov. Janet Napolitano vetoed a dozen weapons bills, but resigned in January 2009 to become U.S. homeland security secretary. GOP Secretary of State Brewer then became governor.
Brewer, during her first year in office, signed a bills allowing loaded guns in bars and restaurants and prohibiting property owners from banning guns in parking areas, so long as the firearms are locked in vehicles, the Republic reported.