Lynne, who also founded the The Travelling Wilburys with George Harrison, Bob Dylan, Tom Petty and Roy Orbison, is headlining the BBC Radio 2 show in September.
He said: "I haven't performed live in quite some time, and I know the fans have asked for it a lot over the years. It's very exciting to come to Hyde Park with Radio 2 and do something this big, and I'm very much looking forward to playing my ELO songs for everyone."
DJ Chris Evans announced the news on his breakfast show, saying: "ELO was the first band I ever saw live. Jeff Lynne lit up the eyes of a fourteen year old that have been burning as brightly as the sun ever since. ELO are my generation's Beatles and I cannot believe we've got the main man playing our Festival In A Day - not to mention what was already a stellar line-up before today's announcement of this year's headline act."
ELO - or Electric Light Orchestra - released a string of hit singles in the 1970s and 1980s including Mr Blue Sky, Wild West Hero and Xanadu with Olivia Newton-John.
Coverage of the Sunday September 14 gig will be available to watch on the BBC Red Button, the iPlayer and the Radio 2 website.