The bill was signed as the National Rifle Association's lobbyist, Marion Hammer, looked over Bush's shoulder.
It is not likely to boost gun sales by much, if at all, when it goes into effect Oct. 1.
Floridians already have some of the most gun-friendly laws in the nation. They have the right to carry concealed weapons and can get around background checks if they buy their firearms at gun shows.
The state also has reciprocal agreements with other states honoring concealed-weapons permits. Bush signed that bill into law April 20, 1999, also with Hammer in attendance.
Rather than a gun law, the new law is more of a tough-on-crime bill. It describes itself as letting people "meet force with force, including deadly force."
It applies when they are under an attack that threatens death or bodily harm.
Residents will no longer have a duty to retreat when they encounter a threat outside the home. The bill said a Floridian has the "right to stand his or her ground."
The new law expands an existing statute based on the "castle doctrine" that allows residents to use deadly force inside their homes.
"I think the message to criminals is going to be, you break into a home, you run the risk of being shot. You attack people on the street, you run the risk of being shot," said Hammer, a former president of the NRA.
"Existing law is on the side of the criminal. The new law is on the side of the law abiding victim," she said in a statement.
Bush said the new law was needed because the old law requires someone who is threatened to retreat.
"Under a life threatening situation, you have to retreat and put yourself in a very precarious condition. It defies common sense," the Republican governor said.
One of the opponents of the law is the father of a teenage boy who was killed a year and a half ago while playing door-knocking pranks in a Boca Raton, Fla., neighborhood.
Investigators said resident Jay Levin heard something outside his door and when he opened it he saw Mark Drewes. He thought the boy was turning toward him, and he shot him in the back.
Levin pleaded guilty to manslaughter and was sentenced to 52 weekends in jail and probation.
The boy's father, Greg Drewes, opposed the bill because he believes his son's killer would have gone free if it had been in effect at the time of the Boca Raton shooting, the Palm Beach Post reported.
"It's a joke. Unbelievable. It's a bad joke," said Drewes of the new law.
"If you shoot somebody in anger, what are you going to say? I made a mistake. I wasn't in any danger. Take me away?" Drewes said. "They're all going to lie. They're all going to say 'I did it to protect myself. I was in fear for my life."
Palm Beach County state Attorney Barry Krischer agreed with Drewes, especially as it would have applied to Levin.
"My belief is that it was reasonable for him to shut the door rather than pull the trigger. He should have shut the door instead of shoot him," Krischer said.
"Under this law he has no obligation to shut the door. Under this law he can stand there and shoot," the prosecutor said.
The bill passed unanimously in the Senate and had an overwhelming majority in the House.
Rep. Dan Gelber, D-Miami Beach, one of 19 who voted against the bill, said it is easy to imagine some unintended consequences.
"Two people in an altercation, that happens every day. Someone thinks you're looking at their wife the wrong way, somebody spills coffee on you, someone bumps into you, someone cuts you off, then all of a sudden they're in a fight, said Gelber. "Do we tell those people that they're supposed to walk away or do we tell them that you're supposed to stand your ground and fight to the death?"
Gelber, a former federal prosecutor, said no one has ever been prosecuted in Florida for lawfully protecting themselves.
Hammer said people shouldn't have to depend on law enforcement to protect them in every situation.
"They're not there when people are attacked. Taking responsibility for your own protection has always been something we've done in this country. All we're doing here is giving law-abiding people the tools that they need once again to protect themselves," Hammer said.
Rep. Dennis Baxley, R-Ocala, a sponsor of the bill who attended the signing, said the law brings Florida into line with other states.
"We're not breaking ground here. We're catching up," Baxley said.
(Please send comments to email@example.com.)
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'
Exploding whale video goes viral on Internet