Cynthia Robinson individually sued Reynolds, the makers of Camel cigarettes, in 2008 on behalf of her late husband, Michael Johnson Sr. He had died in 1996, aged 36, after smoking one to three packs a day for more than 20 years.
The aim of the lawsuit was to stop tobacco companies targeting children with their advertising.
"The jury wanted to send a statement that tobacco cannot continue to lie to the American people and the American government about the addictiveness of and the deadly chemicals in their cigarettes," said Christopher Chestnut, one of Robinson's attorneys.
Robinson's case was one of thousands filed in Florida after the state Supreme Court ruled smokers and their families need only prove addiction, and that smoking caused their illnesses or deaths.
Reynolds' vice president and assistant general counsel, Jeffery Raborn, called the damages "grossly excessive and impermissible under state and constitutional law."
"This verdict goes far beyond the realm of reasonableness and fairness, and is completely inconsistent with the evidence presented," Raborn said. "We plan to file post-trial motions with the trial court promptly, and are confident that the court will follow the law and not allow this runaway verdict to stand."
The Pensacola jury took 11 hours to reach their decision to award Robinson $7.3 million (5.3 million euros) and the couple's son $9.6 million in compensatory damages and a further seven hours to decide on the $23.6 billion in punitive damages. The decision was announced late on Friday.
RJ Reynolds brands include Camel, Kool, Winston, Salem and Pall Mall. The company merged with Brown and Williamson, the US operations of British American Tobacco in 2004.
jm/av (Reuters, AFP, AP)