Here are the hurdles they'll have to jump in the long royal steeplechase to the altar.
Ask Granny's permission
Given his position as fifth-in-line to the throne (shortly to be sixth, after the birth of William and Kate's next baby), Harry would have to ask the Queen for permission to marry Meghan. Under the Succession to the Crown Act 2013, the first six people in the line of succession must ask the monarch to allow them to wed.
Book a place in Granny's diary
There is also the question of the packed royal diary for the whole royal family, who are generally booked-up several years in advance.
"Everyone thinks the engagement will come," says Hugo Vickers, biographer of the Queen Mother and Camilla, Duchess of Windsor. But it's likely to be after the Queen and Prince Philip celebrate their 70th wedding anniversary on November 20.
The background check
Even with Prince Philip's royal blood, there were raised eyebrows when he got engaged to the Queen. Despite his heroic naval service during the war, petty-minded courtiers were concerned about the Nazi aristocrats who had married the prince's sisters.
Reporters have already trawled through Meghan Markle's distant relations to find some rotters. But, in these more broad-minded days, we are not held responsible for our relatives' behaviour.
The exes
Edward VIII had to abdicate to wed twice-divorced Wallis Simpson in 1936. Even 20 years later, Princess Margaret felt unable to marry divorced Captain Peter Townsend.
Divorcee Meghan was married to Trevor Engelson, an American film and television producer, from 2011 to 2013. When the divorced Prince Charles married the divorced Camilla Parker Bowles in 2005, it was a civil ceremony, followed by a blessing in St George's Chapel, Windsor.
However it is now possible for divorced people to be married in the Church of England.
God check
Members of the royal family used to lose their place in the line of succession if they married a Catholic. Meghan's father is Jewish, and she attended the Catholic Immaculate Heart Convent in Los Angeles. But since 2015, royal family members have been allowed to marry Catholics without jeopardising their position. Any child of Harry and Meghan, if brought up Catholic, would be banned from succeeding to the throne (an unlikely prospect anyway) as the monarch remains the Supreme Governor of the Church of England.
The official interview
It seems likely that Prince Harry would do an official engagement interview on television, as his brother and father did before him.
Set a date, choose a dukedom
Prince William's engagement followed much the same pattern as his father and grandmother. The news was announced by Clarence House and they married five months later in Westminster Abbey.
Harry is likely to get married in Westminster Abbey, too, with a similar engagement period to his brother, father and granny, of four to six months. Just like his grandfather Prince Philip, William accrued new titles on the morning of his wedding: Duke of Cambridge, Earl of Strathearn and Baron Carrickfergus. Prince Harry can expect similar treatment.
Put a ring on it
William gave Kate Princess Diana's engagement ring. Keen royal-watchers should look out for a tall, ginger 33-year-old in upmarket jewellers.
