The employees will be able to keep their benefits for up to a year, including medical, dental and life insurance.
The move will take effect on 19 April.
The Service Trades Council, a coalition of unions representing Disney World workers, said in a statement: "The union agreement provides stronger protections and benefits for 43,000 union workers at Disney than virtually any other furloughed or laid-off workers in the United States."
The company will keep 200 workers to perform "essential duties". They will be offered positions based on seniority, the union said.
Disney World is expected to furlough up to 77,000 workers in all. The Orlando Sentinel reports that adding that number to unemployment figures would triple the city's jobless rate from 2.9 per cent in February to 8.5 per cent.
Sean Snaith, an economist at the University of Central Florida, told the paper that the move would have a knock-on effect for the area's airport and car rental companies.
He said: "All the suppliers that will normally actively be engaged with Disney have gone idle as well."
In a statement the company said: "The Covid-19 pandemic is having a devastating impact on our world with untold suffering and loss, and has required all of us to make sacrifices. Over the last few weeks, mandatory decrees from government officials have shut down a majority of our businesses."
Florida has recorded at least 18,978 cases of the coronavirus, with at least 445 deaths.
The state's governor, Ron deSantis, has faced criticism for not doing more to shut down activities earlier, including allowing spring break parties. Several spring breakers later tested positive for Covid-19.
Mr DeSantis, a vocal supporter of Donald Trump who has been praised for his performance by the president, said last week that he still believed schools in Florida could reopen in May. Anthony Fauci, one of the administration's lead scientists on the coronavirus task force, has said he does not expect schools to be able to open before autumn.
New York City's mayor, Bill de Blasio, said on Saturday that he would keep schools closed for the rest of the year -- although state governor Andrew Cuomo quickly intervened to say that the decision was his to make.
Disney's move comes as the number of people applying for unemployment benefits in the United States continues to spike, with 17 million people filing in the past four weeks.
The Associated Press contributed to this report
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies