The couple giggled over having “podcast voices” and even hummed Christmas songs during the heavily-scripted three-minute trailer.
It is the latest lucrative deal for the pair since they split from the Royal Family and comes after they signed an exclusive Netflix deal.
The couple will produce their own exclusive series which will begin with a holiday special that will be released later this month.
The new project is a multi-year agreement and their programme will “uplift and entertain audiences around the world”, according to Spotify.
The couple said in a statement: “What we love about podcasting is that it reminds all of us to take a moment and to really listen, to connect to one another without distraction.
“With the challenges of 2020, there has never been a more important time to do so, because when we hear each other, and hear each other’s stories, we are reminded of how interconnected we all are.
Their fans were today treated to a trailer of their brand-new Archewell Audio podcast.
It starts will Harry saying: “Shall we start? Ladies first?”
A giggling Meghan added: “No, say it because I think it sounds really nice with your accent.”
Prince Harry then said: “Hi guys, I’m Harry” before Meghan added: “And I’m Meghan” – with the pair choosing not to use their royal titles.
Meghan, in a more serious tone, went on: “One of the things my husband and I have always talked about is our passion for meeting people and hearing their stories.
“And no matter what the story they usually offer an understanding of where someone else is coming from. And in some way, remind you of a story about yourself.”
Harry chipped in and added: “And that is what this story is all about. To bring forward different perspectives and voices that perhaps you haven’t heard before.
“And find our common ground. Because when that happens change really is possible.”
It is available on the streaming service, accompanied by a short description which reads: “Prince Harry, the Duke of Sussex and Meghan, the Duchess of Sussex, present Archewell Audio. Coming soon to Spotify.”
Their podcast will be available for free through Spotify – which also offers more than 1.5 million podcast titles such as “The Michelle Obama Podcast”.
The Duke and Duchess of Sussex may live in California but the power of their voices rests in their status as citizens of the world.”Dawn Ostroff, Spotify’s chief content
Their first podcast installment will be a holiday special featuring “stories of hope and compassion” to celebrate the new year.