The source said they have "no plans" to use social media for their new Archewell Foundation and were "very unlikely" to return to platforms.
It is believed the couple have become discouraged by the hate they have received through social media.
In a past interview Meghan called online trolling "almost unsurvivable".
Despite removing themselves from the social media world, the couple still hold contracts and upcoming projects with Netflix and Spotify.
However, critics wonder how the couple will attract audiences if they are to "justify" their new Spotify deal.
Recently, on the Teenager Therapy podcast, Meghan spoke about being "the most trolled person in the world", calling the experience isolating.
She also faced online abuse when pregnant.
"I'm told that in 2019 I was the most trolled person in the entire world, male or female,' she said.
"Now, eight months of that I wasn't even visible — I was on maternity leave or with a baby," she said.
"If people are saying things about you that aren't true, what that does to your mental and emotional health is so damaging … That's so big, you can't even think of what that feels like."
During their time sharing through the Kensington Palace's social media account she received 5000 abusive and racist tweets in two months.
In the 2019 documentary "Harry and Meghan: An African Journey", the couple touched on their struggles over "unfair" scrutiny.
Harry told presenter Tom Bradby how he still struggles to deal with the "incredibly raw" death of his mother and admitted his personal mental health struggles.
Before marrying Harry, Meghan was an avid social media users with 1.9 million followers on Instagram, 350,000 Twitter followers and 800,000 likes on Facebook.
She also had her own website and blog called "The Tig".
