The contest came to an end on Sunday as a noon deadline passed for county election officials to submit the results of a hand recount that showed Scott leading Nelson by about 10,000 votes, or 0.12 percentage points.
The hand recount was ordered after a machine recount showed the two candidates separated by only about 12,600 votes, or 0.15 points.
Shortly after the results came in, Scott released a statement saying Nelson had called to concede.
"Things worked out a little differently than Grace and I had hoped, but let me say, I by no measure feel defeated," Nelson said in a video statement on Sunday. "I was not victorious in this race but I still wish to strongly re-affirm the cause for which we fought: A public office is a public trust."
Nelson acknowledged that he had been "heavily outspent" by Scott, who pumped more than $51 million of his personal fortune into his Senate bid. He also warned of a "gathering darkness in our politics."
"My hope today can be found in the words of John F. Kennedy, who said civility can guide us through that darkness to a safe and sane future," Nelson said.
The latest results cemented Scott's victory in a hard-fought race that stretched nearly two weeks past Election Day, when he appeared to edge out Nelson by less than 1 point.