The measure, which passed the Legislature overwhelmingly earlier this year, says that people who are under attack do not have to retreat before responding. They have the right to "meet force with force, including deadly force if they reasonably believe it is necessary to do so."
Florida residents already have that right in their homes. The bill, which takes effect Oct. 1, extends the right to public spaces, such as the street or a place of business, CBS News Correspondent Jim Acosta reports.
"It says to people: You can stand your ground and if you feel reasonably threatened that harm is going to come to you," CBS News Legal Analyst Andrew Cohen said. "You can fire away."
Supporters said the measure brings Florida in line with a number of other states.
"When you're in a position where you're being threatened ... to have to retreat and put yourself in a very precarious position, you know, it defies common sense," Bush said.
The measure was the NRA's top priority this year, said the group's lobbyist, Marion Hammer. "Now, the law and their government is on the side of law-abiding people and victims, rather than on the side of criminals," she said.
Opponents of the bill warned that it would lead to a "Wild West" atmosphere in Florida, where gun-toting people would have shootouts in public places simply because they could. No one will ever back down, opponents argued.
"You are telling people when they are in the midst of an emotional moment ... you can stand your ground until death happens," Rep. Dan Gelber, a Democrat, said during House debate on the bill earlier this month.
Former Miami prosecutor Katie Phang told CBS' Acosta that the law undermines some judicial sensibility. When juries used to decide who is guilty, now the power has shifted.
"Who's going to start claiming self-defense? Who's gonna start saying what's reasonable and what wasn't?" Phang said. "There used to be a time when the jury decides that. But now, it will be who has the better aim, in my opinion."
But Republican Rep. Dennis Baxley, the bill's sponsor in the House, said the measure wouldn't result in free-for-all gun battles, in part because of laws that prevent people from carrying guns in many instances, such as into a stadium or a bar.