Mr Scott beat Mr Nelson narrowly after an expensive race that ranks as one of the most expensive in US electoral history.
Mr Gillum called Mr DeSantis to concede late Tuesday evening, but vowed to continue to fight for causes he believes in.
In down-ballot races, Democrats flipped two House seats from Republicans, with Democrats Debbie Mucarsel-Powell and Donna Shalala now set to become US representatives in January.
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