The prince, 33, and the "Suits" actress, 36, are expected to tie the knot in a ceremony next spring, according to a statement from Clarence House.
Harry and Markle kept their relationship fairly secret until the prince proved his loyalty by blasting the hateful comments being directed towards his new love.
A series of introductions to senior members of the royal family began as early as last autumn, when she met Prince Charles for the first time.
For his part, the prince had never seen Suits, the American legal drama in which Ms Markle stars, and had never even heard of her before they met.
He said being away allowed them to get to know each other without the usual pressures of royal life.
"He got on one knee", Markle said.
Ms Markle's parents, Thomas Markle and Doria Ragland, said their daughter was a "kind and loving person" and they were "incredibly happy".
That statement said the couple were "a few months into a relationship" and it was "not right" that Ms Markle should receive such treatment.
The sleek coat Markle stepped out in is by Canadian brand Line The Label-whose site already temporarily crashed just minutes after the engagement photo call took place (the power of royal style).
"What I would also like to say is that I really do admire the way that Harry and his brother have drawn attention to mental health conditions all across the country".
The pair were introduced in July 2016 by mutual friends in London, Markle confirmed in September.
"At the end of day I'm really just proud of who I am and where I come from and we have never put any focus on that", she said. She was born and raised in Los Angeles and graduated from Northwestern in 2003. Her father was a TV lighting director for soaps and sitcoms and her mother a clinical therapist.
In 2011, she married film producer Trevor Engelson but they divorced two years later.
There is a long-running custom barring royals from marrying Catholics and divorcees.
Shortly after the announcement, a Buckingham Palace spokesman told CNN that Harry's grandmother, Queen Elizabeth II, and her husband, the Duke of Edinburgh are "delighted" for the couple and "wish them every happiness". Despite its popularity, however, it is speculated that Prince Harry will ditch Westminster Abbey since it was home to the funeral of his beloved mother Princess Diana in 1997.
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