With all precincts reporting, Gimenez captured 51 percent of the vote to Robaina's 49 percent in the election Tuesday, The Miami Herald reported.
"I am happy," Gimenez said. "But I also know that come tomorrow I have a lot of work to do."
The vote ends a 2 1/2-month campaign to select a successor to former county Mayor Carlos Alvarez, ousted in March in a recall election.
Gimenez's agenda for the next year includes closing a budget gap that could balloon to more than $300 million, reorganizing and streamlining county government, renegotiating 10 labor contracts and initiating a number of reforms, including a term limit of eight years for county commissioners, the Herald said.
Race results will be official Friday when the vote is certified by the county canvassing board, the Herald said.
Gimenez said he hopes to go to County Hall Wednesday to begin work.
"Even though I am not officially the mayor, I need to get ahead of this," he said. "If they allow me to go in, I will."