Oprah Winfrey has bought a gift for Prince Harry and Meghan, Duchess of Sussex's newborn son Archie.

The royal couple welcomed their first child, a son named Archie Harrison Mountbatten-Windsor, on May 6, and Oprah has said she's got a gift ready to send the newborn tot, although she hasn't had a chance to mail it yet.

Speaking to Us Weekly magazine, she said: ''I'm not telling [what it is]. I haven't sent it yet.''

Oprah did confirm to the publication that she has already purchased the gift.

Harry, 34, and the 37-year-old former 'Suits' actress announced their son's arrival earlier this month.

In a post on Instagram, they wrote: ''We are pleased to announce that Their Royal Highnesses The Duke and Duchess of Sussex welcomed their firstborn child in the early morning on May 6th, 2019. Their Royal Highnesses' son weighs 7lbs. 3oz. The duchess and baby are both healthy and well, and the couple thank members of the public for their shared excitement and support during this very special time in their lives.''

And Meghan - who was known as Meghan Markle before marrying Harry in May last year - said following the birth that her son has been a ''dream''.

She told reporters: ''He's been the dream, so it's been a special couple of days. He has the sweetest temperament. He's really calm. ... [Motherhood is] pretty amazing and I have the two best guys in the world, so I'm really happy.''

The royal couple said before Archie's birth that they would be keeping the birth private, and wouldn't be posing for photos outside the Lindo Wing - which is the private maternity ward at St Mary's Hospital in Paddington, London - like Prince Harry's brother Prince William had done for his three children Prince George, five, Princess Charlotte, three, and 12-month-old Prince Louis, whom he has with his wife Catherine, Duchess of Cambridge.

And Oprah had commended the pair's decision, saying she was ''so proud'' of Meghan for having the bravery to go against tradition.

She said earlier this month, just a few days before Archie's birth: ''Oh my God! I'm so proud of her decisions.

''To be able to stand up and say this is what I really want for my baby and my family and now I'm going to do it a different way when it's been done that way for a thousand years? I'm just so proud of her.''