The couple shared the news in the engagement announcement section of the London Times, Sky News reports.
Daley, 21, and Black, 41, have been dating for about two years and live together in London, according to Sky News. Daley came out as bisexual in a YouTube video posted in December 2013, in which he said he had fallen in love with a man but didn't identify Black by name.
Daley won a bronze medal at the 2012 London Olympics and plans to compete in Rio next year. Black is best known for writing the screenplay to Milk, for which he won an Academy Award in 2009.