Cyprus has enforced a "near complete ban" on flights since 21 March, which the FCO said had limited commercial options for Britons to get home.
Only humanitarian and cargo flights are being allowed to arrive on the island.
"We know this is concerning for British people trying to leave Cyprus," said the FCO.
"The UK government is working closely with airlines, the Cypriot authorities and other governments to make sure options are available for you to return to the UK as soon as possible."
The repatriation flights will start on Saturday (25 April) and continue through to 30 April, said the FCO in an update issued on Thursday afternoon (23 April).