Royal expert Chris Ship said the Sussexes jumped out of the frying pan into the fire after their historic announcement in January.
The pair initially settled in Canada before moving to Los Angeles, California, the US.
Mr Ship told ITV’s Royal Rota podcast: "[Los Angeles] is filled with celebrities and therefore filled with the paparazzi who are trying to make money from getting pictures of the celebrities.
"There is a kind of irony of them running away from a royal life where Harry didn’t want to be under the spotlight anymore."
Speaking to his guest on the podcast, ABC News Foreign Correspondent Maggie Rulli, he said: "If I were to ask you ‘where in America are the most paparazzi photographers?’ you would say Los Angeles."
Ms Rulli agreed, saying that LA seemed a poor choice for a couple who wanted to avoid the spotlight: "I think it is interesting where they chose to move because Los Angeles clearly has the most paparazzi."
She said it was hard to describe to a British audience just how many celebrities are to be found in one small area of LA.
"Every A-list celebrity is walking by," she said, "so you have paparazzi on every corner looking for these celebrities.
"It is such a culture there… trying to get that photo!”
She did accept, however, that the couple’s new $15 million (£11.2m) home in Santa Barbara, where they have settled after a few months staying in Tyler Perry’s Beverly Hills mansion, is a little more quiet and peaceful than Los Angeles itself: "Harry and Meghan chose where they are staying an hour to two hours drive to LA,” she said, “so they did get away a little bit.
Describing the area where the couple have settled as a sunny version of Cornwall, she added: "The area where they are it does not really feel like a city – it has a beautiful coastline."
The area is noted for being a secluded bolt-hole for US celebrities who want to avoid the full glare of the spotlight.
Meghan has told US journalist Gloria Steinem that she’s glad to be home in the US “for so many reasons”.