The winner will be able to spec the car themselves.
The all-new sports car, worth £62,995 before options, was the final prize in the televised appeal. The draw, open to anyone over the age of 18, runs until 2pm on April 30. More information can be found here.
The winner of the competition will have the chance to spec the car completely themselves, choosing from more than 40,000 available paint colours, and a wide selection of wheels, interior trims, and accessories. The competition winner will also be invited to tour Morgan's historic factory in Malvern.
What's more, Morgan will pay towards the winner's first year of road tax and insurance on the car, along with servicing for two years.
"We are all aware of the devastating impact the current situation is having around the world, at every level of society," said Steve Morris, chairman and CEO of Morgan Motor Company. "On behalf of the Morgan Motor Company, I am particularly thankful to all of the key workers around the world who continue to keep our communities going.
"I'm proud that we are able to support the global relief effort, as part of BBC's 'The Big Night In', with the donation of a brand new Morgan Plus Four.
"Any Morgan sports car is unique and desirable, and we hope that by offering a new Plus Four as a prize, we will be able to raise significantly more funds towards the global relief effort, than the value of the car itself."
The Morgan Plus Four is the brand's first four-cylinder, turbocharged car – the engine being a 2.0-litre from BMW putting out 255 bhp – and is based on the company's new aluminium architecture. All-in-all, just three percent of the outgoing Plus 4 (note the subtle name change) has been carried over to this new model.