The band will play hits from across their four-decade career, including Wild Boys, Rio and tracks from their current album, Paper Gods.
BBC Radio 2 will broadcast the concert live, while highlights will be shown on BBC One on Sunday, 5 June.
The gig will follow a day of musical events across the UK.
Amateur and professional musicians alike will be encouraged to take part, and Duran Duran will act as ambassadors for the event.
"We're really proud to be ambassadors for BBC Music Day and to bring the Paper Gods tour to the stunning surroundings of the Eden Project," said the band, in a statement. "We've wanted to play there for many years.
"We love the idea of BBC Music Day, it's a fantastic way to bring people together across the country and to promote live music. So, whether it's taking part in one of the events or watching or listening the artists who are part of this year's celebration, we hope everyone gets involved."
BBC Music Day launched last year, billed as a "UK-wide celebration of sound".
Events included a day-long musical relay along the length of Hadrian's Wall, and Manic Street Preachers performing to 10,000 people at Cardiff Castle.
A world record for the longest distance between singers of a duet was also set - as classical musician Shan Cothi in Cardiff sang the Welsh hymn Calon Lan with Andres Evans, a member of the Welsh community in Patagonia - 12,120 kilometres away.
Full details of the 2016 programme - including support acts for Duran Duran - will be announced in the coming weeks
Tickets for Duran Duran's show go on sale via the Eden Project website on Monday, 18 April
Pop group Duran Duran will headline a concert at Cornwall's Eden Project at the culmination of BBC Music Day on Friday, 3 June.