Wriggling around in the Duchess's lap, Archie provided able assistance turning the pages before comically proving the old adage of 'never work with children or animals' right, by reaching for a different book and throwing it on the floor.
"Let's finish this one first?" the Duchess told him gently, picking the book up and looking into the camera in amusement as Prince Harry tried to suppress his laughter.
At one point, Archie appeared to start grizzling before being cheered by the pictures in front of him and beginning to giggle as his mother kept up a running commentary of "what happens next? Can you turn the page?" and quacking in his ear to entertain him.
As he turned the final page in his book, the duchess told baby "Arch" he had done a "good job!" while the duke cheered "bravo!" from behind the camera.
Archie appeared to be trying to talk, making a "dada" sound - possibly for "duck" or "daddy" - at the end of his starring role, trying to chew the cardboard pages for his grand finale.
A spokesman for the Sussexes said: "As they celebrate this family moment, the Duke and Duchess wanted to continue to raise awareness around the urgency of bringing food and learning resources to millions of children. "The Duchess chose to read one of Archie's favourite stories, 'Duck! Rabbit!'"
The simple storybook for small children is based on the optical illusion of the rabbit and the duck, asking young readers to see it from both perspectives and decide which animal they can see.
The book was decorated with a sticker reading "Archie's Book Club". It is thought that the book was a gift from Oprah Winfrey, whose eponymous book club uses similar stickers.
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The Duchess, wearing a casual denim shirt, held Archie on her lap for story time, letting him leaf through the pages as he enjoyed himself. The video gave a glimpse into their new lives in LA, with Archie wearing a white babygrow in the hot weather.
The video was launched on the Save the Children Instagram page in the US and UK, with the British arm of the campaign being led by Poppy Delevigne.
Previous celebrities who have shared stories include Dame Helen Mirren, Julie Walters, Stephen Fry, Eddie Redmayne, Lily James, Joely Richardson and Jude Law.
The Princess Royal is patron of Save the Children, having worked with the charity for 50 years.
In a post launching the video, Save the Children said: "Duck! Rabbit!" with Meghan, The Duchess of Sussex (and Harry, The Duke of Sussex behind the camera), read to their son Archie for his 1st birthday. Happy Birthday, Archie!
"Thank you #DuchessMeghan for helping us to raise urgent funds for our coronavirus appeal."
Sharing details of how to donate to support vulnerable families around the world via their website or text, the charity added: "As the world grapples with the coronavirus pandemic, children's lives are being turned upside down.
"By donating to Save with Stories, you can support the most vulnerable families in the UK and around the world by helping to provide early learning packs, supermarket vouchers, essential household items and virus protection.
"Together, we can help families get through this."
The Sussexes are celebrating Archie's first birthday while under lockdown in America, likely to hold a small party as a family of three.
The couple have made Los Angeles their home and they and other residents of California have been living under a "stay-at-home" order made by the state's governor Gavin Newsom.
The Royal Family sent public birthday wishes to Archie via its social media accounts sharing photographs of him at his Windsor Castle christening and meeting the Queen as a newborn.
Archie was born on May 6 2019 at 5.26am, weighing 7lb 3oz. A few days later, he appeared on camera wrapped in a blanket, and met the Queen and Duke of Edinburgh for the first time.
Meghan's mother Doria Ragland, a yoga instructor and social worker, was pictured at the royal gathering.
Fans had been hoping the couple follow royal tradition and release a picture of Archie, who has rarely been seen in public, to mark the birthday milestone.
He received his greatest exposure when the Sussexes took their son on his first royal tour, visiting South Africa last autumn when he was four months old.
The royal baby received a welcome kiss from Archbishop Desmond Tutu when Harry and Meghan introduced him to one of the heroes of the anti-Apartheid movement.
Archie made an impression with the Archbishop's daughter Thandeka Tutu-Gxashe, who joked the young royal favoured "ladies better" when she caught him glancing in her direction and Meghan declared "he likes to flirt".
Earlier in 2019 Archie was photographed in his mother's arms while his father took part in a charity polo match.
Meghan and Harry are the subject of a new biographical book, due for publication in August, which its authors have said they want to be a "definitive story" about the couple.
