Tice spent the money on Miami Dolphins NFL season tickets, professional football memorabilia, dining and repaying personal debt, investigators said.
Deputies said Tice was relieved of his position at the museum in February 2016 for an unrelated matter.
"When you're elected to office, you have the public's trust," Brevard County Sheriff Wayne Ivey said during a Thursday news conference. "They wouldn't elect you if they didn't trust you. And when you violate that trust, it sends a horrible message.
"When you're taking money meant for a charitable organization and you're using it for personal gain or watching a football team play, there's no explanation for that," Ivey said. "It's absolutely despicable."
Tice was booked into the Brevard County Jail on charges of scheme to defraud under $20,000, communications fraud, depositing an item with the intent to defraud and grand theft. He was released after paying a $20,000 bail.
Although the allegations are unrelated to Tice's duties as deputy mayor, West Melbourne Mayor Hal Rose called the accusations "shocking" and said he was "saddened by the course of events."
A spokeswoman for Gov. Rick Scott said his office is investigating the allegations.
"Gov. Scott expects all elected officials to behave ethically and responsibly," she said. "Our office is reviewing the details, and we will keep you updated on any action taken."