The Sussexes' post read: "Thank you for your support, inspiration and commitment to the good in the world."
The royal expert continued: "Today marks the end of that transition period, where they were meant to officially step down, but of course due to the coronavirus outbreak they haven't been able to do that. They've effectively put these all on ice.
"I think they regarded it as not only inappropriate to be rebranding at a time like this, but equally, they aren't going to get the column inches they wanted."
The couple had planned on splitting their time between Canada and the UK before the coronavirus forced them to speed up plans to move to Meghan's birthplace of Los Angeles.
The expert added: "We understand that this big move was done rather in a rush. They took one of the last flights of Canada to get to America and they're currently renting and looking somewhere, perhaps on the beachfront in Malibu.
"But all of the plans about them launching this new charity, have been put on ice."
Discussing why the pair chose to uproot with baby Archie to Los Angeles, Ms Tominey said: "It's her hometown, it's where she grew up, where all her friends are based.
"They've announced they are being represented by that US agency Sunshine Sachs.
"They've said they will no longer be represented by the royal communication office, essentially they're setting up shop as celebrities."
She added: "They're still known as the Duke and Duchess of Sussex but they can't use that royal branding, so they're on the red carpet with the rest of the A-listers."
It comes as Meghan's first project away from the royal family was announced by Disney as a documentary on Elephants.
Meghan who voices over the film was said to have accepted the project in exchange for a donation to Elephants Without Borders, a non-profit organisation in Botswana that aims to protect the species from poaching.
The duchess allegedly landed the role after her husband, Prince Harry, talked up Meghan's interest in narrating a project to Disney's then-CEO Bob Iger at the London premiere of The Lion King last July.
The early reviews for the documentary have mixed, with many British reviewers criticising the duchess.
Ed Potton from The Times wrote: "Meghan is swapping pomp and circumstance for schmaltz and cheesiness.
"The departing Duchess of Sussex narrates Disney's tale of a herd of elephants crossing the Kalahari Desert from the Okavango delta to the Zambezi River, and boy does she lay it on thick.
Last year Meghan joked that she and Harry attended the premiere of The Lion King in London, to "pitch" for work, footage from the event revealed.
Prince Harry was also filmed showing off his wife's voiceover skills to former Disney CEO Bob Iger at the event in July.
In the video, Prince Harry pointed to his wife and said: "You do know she does voiceovers?"
A surprised Mr Iger replied: "I did not know that"
The duke and duchess have put all Hollywood plans on the back burner, as they keep a low profile in Los Angeles during this uncertain time. Yesterday on This Morning, royal expert Camilla Tominey said that their "rebrand as celebrities" has effectively been "put on ice."
Ms Tominey told hosts Phillip Schofield and Holly Willoughby that Meghan and Harry have decided against rebrand because they wouldn't get the "column inches" they wanted, as well as feeling it's "inappropriate" to rebrand at this time.
Speaking on the couple's cryptic final "royal" Instagram post, Phillip said that it was as though the couple were "signing off".
Ms Tominey agreed, replying: "Wasn't it? Very much so. What's interesting is, this week they were meant to be launching their life as non-royals.