The broadcast, on BBC Radio 4 and the World Service, will mix recordings of the original speech with excerpts spoken by guests.
Listeners will hear the entire speech with other names taking part including Nelson Mandela's granddaughter Ndileka, and Malala Yousafzai, the 16-year-old Pakistani schoolgirl shot by the Taliban for going to school.
There will also be contributions from Congressman John Lewis, who was then a civil rights activist and also spoke that day, and singer Joan Baez and writer Maya Angelou.
Dr King gave the speech in 1963 during a march in Washington DC supporting proposed civil rights legislation. He won the Nobel Peace Prize in 1964.