His margin has shrunk with each victory — he beat Alex Sink by 1.2 percentage points in 2010, Charlie Crist by 1 point in 2014, and Mr. Nelson by 0.1 of a point. But this year, for the first time, he obtained a majority of the vote, 50.1 percent.

Behind Mr. Scott’s victories lies his vast personal wealth. He and his wife, Ann, put more than $70 million into his first campaign for governor and nearly $13 million into his second; this year, Mr. Scott spent more than $50 million on the Senate race. But as a candidate, Mr. Scott, who is not known for his charisma, did more than just open his checkbook: He campaigned incessantly and stayed relentlessly on message, casting Mr. Nelson as a do-nothing has-been who had to be retired.

Mr. Nelson admitted in a concession statement that “things worked out a little differently” than he had hoped.

“I by no measure feel defeated, and that’s because I’ve had the privilege of serving the people of Florida and our country for most of my life,” he said. “To all Floridians, whether you voted for me, or for my opponent, or you didn’t vote at all, I ask you to never give up this fight.”

He did not mention Mr. Scott by name.

Though Mr. Nelson, 76, was a three-term incumbent from Orlando, he had less name recognition than Mr. Scott, 65, a multimillionaire former hospital executive from Naples. Mr. Scott made much of his wealth leading the Columbia/HCA hospital chain, which during his tenure was fined $1.7 billion for Medicare fraud, an issue that forced him out of his job.

Mr. Nelson, a centrist who was first elected to the State House in 1972, was not particularly exciting to the increasingly young, progressive Democratic base, and he never quite seemed comfortable seizing the spotlight.