His lecture, to be broadcast later this year, is part of a raft of new BBC Radio 4 programmes unveiled on Monday.
They include Glenda Jackson's return to acting, in a drama based on a cycle of 20 novels by French writer Emile Zola, and a Late Night Woman's Hour.
Also announced is that Miles Jupp is to take over as the new host of BBC Radio 4's comedy show The News Quiz.
Prof Hawking said he hoped his lecture would "encourage people to imagine and explore the possibilities of science - both the known, and the as yet unknown".
He will also answer some questions sent in by listeners ahead of the recording.
"I will describe the remarkable properties of black holes, including the fact that very small black holes aren't black at all, but glow like hot bodies," he said.
"We should never stop trying to tell these extraordinary stories from science, and I hope my Reith Lecture will enthuse a new generation to develop ideas that will have an impact on our understanding of the world and never to be overwhelmed by the task of discovery."
The BBC Reith Lectures began in 1948, with a talk by philosopher Bertrand Russell. Last year, surgeon Atul Gawande examined the future of medicine. Past lecturers include artist Grayson Perry, politician Aung San Suu Kyi and conductor Daniel Barenboim.
Prof Hawking's lecture coincides with BBC Radio 4's plans to mark the 100th anniversary of Albert Einstein's general theory of relativity.
BBC Radio 4 controller Gwyneth Williams, who announced the new season along with BBC director general Tony Hall, said: "I know that our discriminating audience will be inspired by Prof Hawking's magnificent challenge "never to stop trying to tellâ€¦ extraordinary stories from scienceâ€¦ and never to be overwhelmed by the task of discovery'."
The rest of the season includes:
Double Oscar winner Glenda Jackson's return to acting after more than two decades in politics comes in an adaptation of Emile Zola's 20-volume novel series Les Rougon-Macquart.
Entitled Blood, Sex And Money, the series is described as "a multi-stranded immersive experience that draws us into 19th Century France". There will be three seasons, broadcast at six-monthly intervals, with the first beginning on 21 November.
Jackson is cast as 104-year-old Adelaide Fouque alongside Robert Lindsay, Georgina Campbell, Fenella Woolgar and Ian Hart.
Late Night Woman's Hour sees Lauren Laverne join the Woman's Hour team in August for a special series containing "mischievous and unbridled" conversation, during which she will share presenting duties with Jane Garvey. Woman's Hour will continue in its regular slot.
Prof Stephen Hawking is to present this year's BBC Reith Lecture, with a talk on black holes.