The last time this happened, the king abdicated his thrown and the United Kingdom was launched into a constitutional crisis.
Things seem to be going smoother this time, however.
When Edward met Wallis
King Edward was rumored to have multiple affairs with married women both before he became king in January 1936 and after he abdicated the throne on Dec. 10, 1936.
According to an article in Times of London the day after Edward's abdication, royal observers noticed that Edward had dinner with Simpson, her then-husband and several others in May 1936. After that dinner, Simpson started appearing alone at subsequent events.
The article later states how "Mrs. Simpson accompanied his Majesty on his Balkan holiday, and later when she was his guest at Balmoral." The American press reported their burgeoning romance, but it did not become public in Britain until early December, the article stated.
On Dec. 3, Simpson left England and went to France, where Edward joined her after he abdicated the throne. His brother, Prince Albert Duke of York, went on to assume the crown and took the royal name of George VI.
At the time, Simpson was still technically married to her second husband (they did not get divorced until May 3, 1937).
Then-Prime Minister Stanley Baldwin gave a speech at the time of the abdication, saying that Edward had told him weeks before the formal announcement, "I am going to marry Mrs. Simpson, and I am prepared to go," according to The Guardian's account of the abdication.
King George gave his brother the title of the Duke of Windsor, and when he married Simpson in France in June 1937, she became the Duchess of Windsor, though she was never granted the formal "Royal Highness" title.
How Edward and Harry differ
The clearest difference between Harry and his great-grandfather's brother is that Edward was king at the time of his relationship with Simpson, while Harry is a prince and fifth in line for the throne.
As king, Edward was also the head of the Church of England. The Church of England, at the time, did not allow divorced people to remarry if their former spouse was still alive.
That was a problem for Simpson, as both her first husband and second husband were still alive when she was in a relationship with, and later engaged to, Edward in the mid 1930s.
The Church of England didn't formally change this rule for decades. It wasn't until 2002 that the Church of England officially approved a rule change to allow divorcees with living spouses to remarry, according to British newspaper The Telegraph.
Charles and Camilla had dated in the 1970s, before they both married their respective first spouses. Camilla married Andrew Parker Bowles in 1973 and Charles married Diana Spencer in 1981. The Bowles divorced in 1995 and Charles and Diana divorced in 1996.
Charles and Camilla decided against having a religious marriage ceremony in 2005, and Queen Elizabeth, Charles' mother, did not attend the civil ceremony. BBC royal correspondents reported at the time that no official reason was given for the queen's decision.
Times have changed
Markle, an American actress and philanthropist whose first marriage ended in divorce, apparently received the blessing of the queen and royal family.
The official Twitter account of the queen and her husband, Prince Phillip, posted a message this morning, saying they "are delighted for the couple and wish them every happiness."
"We're thrilled. We're both thrilled. We hope they'll be very happy indeed," Charles said in his statement.