The trial will begin next week to carry supplies to St Mary's Hospital on the Isle Of Wight.
Transport Secretary Grant Shapps, speaking at the daily Downing Street briefing, said he had "fast-tracked" the trials.
This follows £28m awarded by the government earlier this year to Southampton and Portsmouth councils to carry out drone operations as part of a wider trial.
It came as part of a new package of measures which will see the transport industry boosting its response to thepandemic.
Thousands of volunteers, vehicles, aircraft and ships from the transport sector - including a Boeing 737 - have been placed on standby as part of a new Transport Support Unit (TSU) to help frontline responders.
They will perform tasks such as moving emergency patients, as well as food and medical supplies.
Highways England vehicles could also potentially be used as mobile COVID-19 testing centres.
Network Rail has 8,500 vans and lorries which could be used to transport essential items during the crisis.
Mr Shapps also confirmed he had made an agreement with France and Ireland to ensure the continued movement of goods including food and medicine.
A total of 26 "vital" freight routes between Britain, France and other European countries are being protected.
"The continued operation of both passenger and freight transport is critically important to our resilience as a country," Mr Shapps said.
The transport secretary also said he would keep "under review" whether to introduce airport scanning for coronavirus, following criticism that those entering the country were not being screened.
However, Mr Shapps said countries including the US which locked down flights early on "have not necessarily weathered the storm of coronavirus any better".
In yesterday's daily briefing, Health Secretary Matt Hancock announced that key workers and their families will now be able to
Mr Shapps today dismissed suggestions the website had crashed, saying it was "simply that the slots for today were taken up".
More than 19,000 people who contracted coronavirus have died in UK hospitals, withannounced today.