In the heartwarming video, shared in support of Save The Children UK, Meghan is seen reading the book Duck! Rabbit! to the tot while Harry films them.
Harry doesn't appear in the clip, but viewers can hear him behind the camera.
What did Phil say?
And daytime TV favourite Phil thought he noticed something strange about the Duke's voice.
Royal expert Camilla Tominey, who was a guest on This Morning, said during the conversation: "It was quite funny to hear Harry in the background, chuckling away."
Phil then said: "It also sounded like he had a Scottish accent at one stage!"
Camilla replied: "Did he? Yes, he seemed to be chirping."
She went on to point out that, in all likelihood, Harry's accent hadn't changed - and put it down to baby talk.
Sounded like he had a Scottish accent.
The royal commentator said: "You know how people speak to babies, though. We all sound ridiculous."
She went on to say she thought the clip was "heart warming", as it showed "lovely chemistry" between Meghan and her son. The three of them are currently living in Los Angeles.
Archie's first birthday
Archie turned one on Wednesday (May 6). A number of his relatives, including great-grandmother The Queen and grandfather Prince Charles, posted touching photos to mark his special day.
Bookies now think Harry and Meghan will announce another baby is on the way this year.
Betting experts think there's a decent chance the Duchess will confirm her second pregnancy in 2020. Betfair has the couple down at 4/7 to announce that Archie's getting a sibling.
A spokesperson for the company said: "Punters are convinced that 2020 may bring further joy for the pair, and they are odds-on at 4/7 to announce another pregnancy in 2020."
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