Harry and Meghan, who announced they are expecting their second child on Sunday, shocked senior royals last year by announcing plans to step back from their roles.
CBS said the interview will be broadcast on March 7.
"Winfrey will speak with Meghan, The Duchess of Sussex, in a wide-ranging interview, covering everything from stepping into life as a Royal, marriage, motherhood, philanthropic work... to how she is handling life under intense public pressure," CBS said in a statement.
"Later, the two are joined by Prince Harry as they speak about their move to the United States and their future hopes and dreams for their expanding family."
Harry and Meghan married in a glittering ceremony in 2018 that captured the world's attention but later gave up their official royal roles following disagreements with other family members and in the face of huge media attention.
The couple moved to California with their infant son Archie last year and have signed a multi-year production deal with Netflix Inc, a major step in their plan to make a living for themselves outside the royal family.
Their relationship with the British press swiftly soured and the couple have launched legal cases against several newspapers.
Last week, Meghan won a privacy claim against Associated Newspapers after its Mail on Sunday paper had printed extracts of a letter she wrote to her father in August 2018.
Winfrey, one of the richest and most influential women in the US, in 2011 ended her top-rated daily television talk show where she interviewed presidents and celebrities.