Doncaster Sheffield Airport (DSA) is to close after its owner said "no tangible proposals" had been received regarding its future ownership.
Peel Group said the closure was due to a "fundamental lack of financial viability".
On Friday, South Yorkshire's political leaders offered public money to keep DSA operating into 2023.
But Peel Group said services at the airport, which employs 800 workers, would wind down from 31 October.
South Yorkshire's Mayor Oliver Coppard said he was "devastated by today's announcement" and angry about the impact the closure would have on local communities.
Mr Coppard said a "big bold offer" had been made to Peel to allow the "time and space to bring in the external interest that we know is out there and get a deal done to save DSA".
He said the offer to use "public money to subsidise Peel Group" had been made "quite reluctantly".
"The Prime Minister, Liz Truss, said herself she wanted to protect DSA, so it's now over to the government to tell us what they might be able to do to keep the airport open," he added.
The airport, which is used by Tui and Wizz Air, flies to destinations including the Canary Islands, Balearics, Greece, Turkey, Poland and the Baltic countries.
Robert Hough, chairman of Peel Airports, said he recognised news of the closure would come as "a great disappointment to many".
Mr Hough said he was grateful to the airport's staff who he said had always been DSA's "greatest asset".
He said the immediate priority would be to "continue engaging closely with them over the next few weeks".
Meanwhile all affected staff at DSA have been offered job interviews by Manchester Airports Group (MAG).
A spokesperson said MAG guaranteed interviews for vacancies across its three airports - East Midlands, London Stansted and Manchester.