The pair became engaged earlier this month and will live at Nottingham Cottage at Kensington Palace, where Harry currently lives.
"Prince Harry has informed Her Majesty The Queen and other close members of his family. Prince Harry has also sought and received the blessing of Ms. Markle's parents," the royal household said in a statement.
The couple will make an official engagement appearance on Monday afternoon before taking part in a broadcast interview which will air in the evening.
Prince Harry and Meghan Markle at the Invictus Games 2017.
Prince Harry and Meghan Markle at the Invictus Games 2017.
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."
Related: Who is Prince Harry's bride-to-be?
Kensington Palace also released a statement on behalf of Markle's parents, Thomas Markle and Doria Ragland.
"We are incredibly happy for Meghan and Harry. Our daughter has always been a kind and loving person. To see her union with Harry, who shares the same qualities, is a source of great joy for us as parents.
"We wish them a lifetime of happiness and are very excited for their future together," the statement ended.
Prince Harry and Meghan Markle attend a Wheelchair Tennis match during the Invictus Games 2017 on September 25, 2017.
Prince Harry and Meghan Markle attend a Wheelchair Tennis match during the Invictus Games 2017 on September 25, 2017.
Harry's brother, William and his wife, Catherine, who also reside at Kensington Palace, shared their joy at the impending union on Monday.
"We are very excited for Harry and Meghan. It has been wonderful getting to know Meghan and to see how happy she and Harry are together," they said in a statement.
Monday's announcement ends persistent speculation over when the 33-year-old prince -- who is now fifth in line to the British throne -- would propose to the actor.
Markle is best known for her role as Rachel Zane in US hit TV series "Suits." Her on-screen father Robert Zane is played by Wendell Pierce.
Photos: Who is Meghan Markle?
Show Caption
5 of 9
Markle played Kirsten in 2015 crime movie "Anti-Social."
Photos: Who is Meghan Markle?
Show Caption
6 of 9
Markle has made a name for herself as an actress and a philanthropist.
Photos: Who is Meghan Markle?
Show Caption
7 of 9
Markle first spoke publicly about her relationship with Prince Harry in an interview with Vanity Fair in September.
Photos: Who is Meghan Markle?
Show Caption
8 of 9
Prince Harry and Markle attended the Invictus Games in Toronto, Canada in September 2017.
Photos: Who is Meghan Markle?
Show Caption
9 of 9
Markle at the ELLE Women in Television Celebration on January 24, 2013 in West Hollywood, California.
Photos: Who is Meghan Markle?
Show Caption
1 of 9
The actress attended Immaculate Heart High School, a private, all-girls Catholic school in Los Angeles. She went by her first name, Rachel, at the time before later using her middle name, Meghan.
Photos: Who is Meghan Markle?
Show Caption
2 of 9
Markle was married to film producer Trevor Engelson for two years before they divorced in 2013.
Photos: Who is Meghan Markle?
Show Caption
3 of 9
Markle at the Some Kind-a Gorgeous Style and Beauty Lounge at the Chateau Marmont on August 26, 2010 in Los Angeles, California
Photos: Who is Meghan Markle?
Show Caption
4 of 9
Markle is best known for her role as Rachel Zane in US hit TV series "Suits." Her on-screen father Robert Zane is played by Wendell Pierce.
Photos: Who is Meghan Markle?
Show Caption
5 of 9
Markle played Kirsten in 2015 crime movie "Anti-Social."
Photos: Who is Meghan Markle?
Show Caption
6 of 9
Markle has made a name for herself as an actress and a philanthropist.
Photos: Who is Meghan Markle?
Show Caption
7 of 9
Markle first spoke publicly about her relationship with Prince Harry in an interview with Vanity Fair in September.
Photos: Who is Meghan Markle?
Show Caption
8 of 9
Prince Harry and Markle attended the Invictus Games in Toronto, Canada in September 2017.
Photos: Who is Meghan Markle?
Show Caption
9 of 9
Markle at the ELLE Women in Television Celebration on January 24, 2013 in West Hollywood, California.
Photos: Who is Meghan Markle?
Show Caption
1 of 9
The actress attended Immaculate Heart High School, a private, all-girls Catholic school in Los Angeles. She went by her first name, Rachel, at the time before later using her middle name, Meghan.
Photos: Who is Meghan Markle?
Show Caption
2 of 9
Markle was married to film producer Trevor Engelson for two years before they divorced in 2013.
Photos: Who is Meghan Markle?
Show Caption
3 of 9
Markle at the Some Kind-a Gorgeous Style and Beauty Lounge at the Chateau Marmont on August 26, 2010 in Los Angeles, California
Photos: Who is Meghan Markle?
Show Caption
4 of 9
Markle is best known for her role as Rachel Zane in US hit TV series "Suits." Her on-screen father Robert Zane is played by Wendell Pierce.
Photos: Who is Meghan Markle?
Show Caption
5 of 9
Harry and his fiancée made their public appearance in September at the Invictus Games in Toronto.
The pair were introduced in July 2016 by mutual friends in London, Markle confirmed in September. Markle is best known for her role on TV show "Suits" as well as her philanthropic work.
The 36-year-old LA native spoke of her royal relationship for the first time earlier this year telling Vanity Fair: "We're two people who are really happy and in love."
Markle, who has been previously married, spoke candidly about the media attention that comes with dating a member of the British royal family, saying it has its "challenges" before adding that she has her "boyfriend's support."
Separately, Prince Harry confirmed the couple were an item last November in a Kensington Palace statement criticizing the "wave of abuse and harassment" his then-girlfriend had faced from media outlets.
The palace rarely puts out such statements, only doing so in recent years to keep the paparazzi from getting too close to Prince George and Princess Charlotte, the children of Harry's brother, Prince William.
The brothers have been much more open about their personal lives than other members of the royal family. In recent months, they spoke publicly about their mother, Princess Diana, on the 20th anniversary of her death.
Prince William and Catherine, Duchess of Cambridge drive from Buckingham Palace in a decorated sports car on April 29, 2011 in London, England.
Prince William and Catherine, Duchess of Cambridge drive from Buckingham Palace in a decorated sports car on April 29, 2011 in London, England.
Monday's announcement sets the stage for the most anticipated royal wedding since William married Catherine Middleton in 2011 in a lavish ceremony at Westminster Abbey.
William and Catherine recently announced they are set to have a third child, revealing the latest addition to the British royal family is due in April next year.
