Divorcee Markle, who has been dating Harry since last summer, is thought to be moving her dogs to the UK amid claims she is planning to live in London with him.
She is said to be trying to ensure her labrador shepherd cross, Bogart, and beagle, Guy, whom she has previously described as "my loves", can join her Britain.
The actress has been rumoured to be leaving for the UK since she and Harry made a public display of affection at the Invictus Games in Canada in September.
In other signs of moving preparations, Markle, who stars in legal TV drama Suits, has been cutting back on her Hollywood commitments.
It is understood that Markle has moved out of her rented Toronto home, where she has been living for the past five years.
She is now shipping her belongings to the UK to embark on a new life with the fifth in line to throne.
Harry made his first public appearance with his American girlfriend at the Invictus Games where they were seen holding hands and exchanging a kiss.
And last month, Harry introduced his celebrity girlfriend to the Queen over tea at Buckingham Palace.
Markle was spotted in Chelsea on Tuesday after a beauty treatment at an exclusive West London clinic where the Beckhams are said to be regulars.
Research has previously indicated that Harry and his girlfriend are distant cousins related through a late 15th Century ancestor of the Queen Mother.
And Markle's great-great-great grandparents, Thomas and Mary Sykes, were born in Yorkshire and left for Pennsylvania in 1869 in search of a better life.
This would not be the first time a royal has married an American. King Edward VIII famously abdicated in 1936 after he married twice-divorced Wallis Simpson.
Prince William and Kate Middleton, now the Duke and Duchess of Cambridge, announced their engagement on November 16, 2010, and married on April 29, 2011.
A Kensington Palace spokesman declined to comment to MailOnline today.
