The controversial television host made the comments as Harry and Meghan dropped plans to use the brand “SussexRoyal” after conceding the word royal could not be used following their decision to leave the monarchy.
A post on their website said on Friday they will not use the branding after the transition in Spring 2020, but highlighted "there is not any jurisdiction by The Monarchy or Cabinet Office over the use of the word 'Royal' overseas".
Responding to the statement, Morgan broadcast his distaste with the actions of Harry and Meghan to his 7.1 million followers.
He said on Twitter: “The staggering disrespect these two keep showing to the Queen is outrageous.
"Who the hell do they think they are?”
In the statement from the Sussexes on Friday, a spokeswoman explained that trademark applications that were filed as protective measures “acting on advice from and following the same model for the Royal Foundation” have been removed.
It is understood the applications were not in the pursuit of commercialisation but to protect the couple’s brand from being exploited.
The duke and duchess’s lives as working royals will end on March 31 when they stop representing the Queen and become financially independent.
Harry and Meghan will embark on a new chapter in North America but sources have stressed they “will be in the United Kingdom regularly” and retain the same charitable goals supporting causes from the Commonwealth to mental health.
The statement on Friday said: “While the Duke and Duchess are focused on plans to establish a new non-profit organisation, given the specific UK Government rules surrounding use of the word ‘Royal’, it has been therefore agreed that their non-profit organisation will not utilise the name ‘Sussex Royal’ or any other iteration of ‘Royal’.
“For the above reason, the trademark applications that had been filed as protective measures and that reflected the same standard trademarking requests as done for The Royal Foundation of The Duke and Duchess of Cambridge, have been removed.
“While there is not any jurisdiction by The Monarchy or Cabinet Office over the use of the word ‘Royal’ overseas, The Duke and Duchess of Sussex do not intend to use ‘Sussex Royal’ or any iteration of the word ‘Royal’ in any territory (either within the UK or otherwise) when the transition occurs Spring 2020.”
The staggering disrespect these two keep showing to the Queen is outrageous. Who the hell do they think they are? https://t.co/QUBSzQ2Fyq— Piers Morgan (@piersmorgan)February 22, 2020
Morgan added on his Twitter: “I'd love to interview [Harry and Meghan].
“My 1st question would be this: 'Why are you putting the Queen through all this extra stress when she's 93, her 98-year-old husband Philip has been very sick, & she's had to fire her son Andrew over a huge ongoing scandal?'”