Gillum, who serves as Tallahassee's mayor, also congratulated Governor-elect DeSantis and thanked his running mate, Chris King, on Twitter Saturday evening.
'This has been the journey of our lives. "We've been so honoured by the support that we've received", Mr Gillum said in a video statement.
US President Donald Trump has repeatedly charged that Florida's elections were marred by vote fraud, but state and local authorities have said there is no evidence of wrongdoing.
Gillum posted the video 11 days after the 2018 midterm elections, when tight margins between the two candidates triggered an automatic machine recount.
After Gillum initially conceded the contest on election night, his subsequent calls for every vote to be counted echoed similar appeals from fellow Democrat U.S. Senator Bill Nelson.
With counties across Florida in the middle of a hand recount for statewide races, Broward thought its recount in the US Senate race was complete on Friday.
State officials ordered a manual recount on Thursday after a machine recount showed less votes in the county than the total number of votes reported to the state on November 10. But campaigns of ideas must give way to governing and bringing people together to secure Florida's future.
For the Senate race, unofficial results show incumbent Nelson trailing Scott by about 12,600 votes out of more than 8.2 million cast, or 0.15 percentage points. The machine recount had DeSantis still leading by over 3,000 votes.
Gillum said in the coming weeks they hope to continue working to bring the Florida election system into the 21st century.
Gillum posted a live video on Facebook on Saturday afternoon in which he congratulated DeSantis. Republican Rick Scott leads in that race. Snipes did insist that the ballots were still in the elections building. Many counties were spending Saturday doing a hand recount in another statewide race. The totals for Nelson and Scott have changed slightly, but not significantly.