The first three episodes of the series will be available on Thursday, the streaming service said, amid widespread speculation over what the couple, the Duke and Duchess of Sussex, will say about the other royals.
Since Harry and Meghan stepped down from royal duties two years ago and moved to California they have delivered stinging criticism of the British monarchy and accusations of racism, accusations that the family has dismissed.
Reuters reports the prince has suggested in interviews he is now barely on speaking terms with the rest of the family, most notably with his father, King Charles, and elder brother, Prince William, the heir to the throne.
"No one knows the full truth," Harry says in the trailer. "We know the full truth."
Buckingham Palace has released no statements about the documentary series and did not immediately respond to requests for comment on Monday.
In the short clip, Harry referred to people working for the royal households briefing journalists about each other, an issue he has previously talked about.
"There's a hierarchy of the family. You know there's leaking, but there's also planting of stories," he says. "It's a dirty game."