Hill, 49, was condemned for the July 29, 1994, shooting deaths of Dr. John Bayard Britton and his bodyguard, retired Air Force Lt. Col. James Herman Barrett, and wounding Barrett's wife, June, outside the Ladies Center in Pensacola.
Hill was pronounced dead at 6:08 p.m., Gov. Jeb Bush's office said.
Death penalty opponents and others had urged Bush to halt the execution, some of them warning Hill's death would make him a martyr and unleash more violence against abortion clinics. The governor said he would not be "bullied" into stopping the execution.
Florida abortion clinics and police were on heightened alert for reprisals.
"Paul Hill is a dangerous psychopath," said Marti McKenzie, spokeswoman for Dr. James S. Pendergraft, who runs clinics in Orlando, Ocala, Tampa and Fort Lauderdale.
Outside Florida State Prison, extra law enforcement officers, explosives sniffing dogs and undercover officers were in place to prevent protests from getting out of hand.
"We don't want an incident of national proportion," Bradford County Sheriff Bob Milner said.
Hill's religious adviser, Donald Spitz, stayed with him until just before his execution.
Since losing his automatic appeals, Hill has not fought his execution and insisted up to the day before his death that he would be forgiven by God for killing to save the unborn.
"I expect a great reward in heaven," he said in an interview Tuesday, during which he was cheerful, often smiling. "I am looking forward to glory."
In that interview, Hill suggested others should take up his violent cause, reports CBS News Correspondent Mark Strassmann.
"I think it was a good thing and instead of people being shocked at what I did, I think more people should act as I acted," he said.
Fringe elements of the anti-abortion movement that condone clinic violence have invited attacks on Web sites that proclaim Hill as a martyr. Members of the mainstream anti-abortion movement have denounced the calls for violence.
One such fringe activist, Drew Holman, told CBS' Strassmann, "Paul Hill should be honored today. The abortionists should be executed and the judges that rule it's okay to kill children should be run out of Dodge."
Most abortion clinics in Florida reached by reporters on Wednesday declined comment. McKenzie said security is always high at their clinics, but they are particularly cautious now because of Hill's call for people to follow his actions.
"The bottom line is when you work in the industry you're aware those people are out there every single day," she said.
Inspired by the 1993 shooting death of another abortion doctor in Pensacola, Hill purchased a new shotgun and went to a gun range to practice. The morning of the murder, as Britton and the Barretts entered the clinic parking lot, Hill shot James Barrett in the head and upper body. He then reloaded and fired again, hitting Britton in the head and arm. Mrs. Barrett was wounded in the arm.
Hill put down the shotgun because he did not want to get shot by police and walked away. When officers arrested him within minutes without incident, he said, "I know one thing, no innocent babies are going to be killed in that clinic today."
Hill was the 57th inmate executed since Florida resumed executions in 1979 and the third in Florida this year.