During the final, which aired Wednesday, host Terry Crews told Williams he had a message from a special fan before playing the clip in which Meghan said she was touched by his story.
Williams spent decades in prison for a crime he did not commit.
"I just wanted to let you know that we have been so moved by your story and we have been cheering you on every week and it's not just because we are partial to the name," said Meghan, making reference to her and Harry's son who is also named Archie.
"So a very special message to you that I'll probably be saying all of my life but on this night, it is specifically for you. Archie, we are proud of you, and we are rooting for you, and we can't wait to see what you do. We are in your corner. Have a good night," said Meghan.
The singer moved judges during his audition when he told them he had spent 36 years in prison for a rape he did not commit.
He said he had watched "America's Got Talent" while incarcerated and hoped to audition for the show one day.
After Williams spent more than a decade in Louisiana State Penitentiary, a maximum security prison with a violent reputation, the Innocence Project took up his case.
The legal nonprofit worked with Williams over the next 24 years and repeatedly requested DNA testing and fingerprint comparisons that could prove his innocence.
Finally, in March 2019, he was cleared of the crime after his fingerprints were submitted into a powerful fingerprint ID system.
Spoken-word artist Brandon Leake was eventually announced the winner of Wednesday's show.
Meghan's message to Williams was her second recent broadcast appearance, as on Tuesday she briefly featured in the Time 100 broadcast special with her husband Harry.
The couple, who now live in California, congratulated those named in this year's Time 100 list of most influential people.
Harry and Meghan also used the opportunity to send a message to voters before the upcoming US election.
"As we approach this November, it's vital that we reject hate speech, misinformation, and online negativity. What we consume, what we are exposed to, and what we engage with online, has a real effect on all of us," said Harry during the video.
"Every four years, we're told, 'This is the most important election of our lifetime.' But this one is," said Meghan. "When we vote our values are put into action, and our voices are heard."