The Daily Mail reports that Harry (33) revealed last year that he had fallen for an American actress, after six months of seeing each other in secret.
The prince reportedly proposed to Markle (36) in London earlier this month.
According to the publication, royal protocol dictated that Harry had to ask his grandmother, Queen Elizabeth, for permission to marry and she agreed in the month in which she celebrated her 70th wedding anniversary.
In a statement, Her Majesty and Prince Philip said they are delighted for the couple and wish them every happiness.
“His Royal Highness The Prince of Wales is delighted to announce the engagement of Prince Harry to Ms Meghan Markle. The wedding will take place in spring 2018. Further details about the wedding day will be announced in due course,” the statement read.
Harry’s American fiancée divorced her first husband in 2013 and will move into Nottingham Cottage in Kensington Palace next to his brother William and sister-in-law Kate.
It also emerged on Monday that Harry asked Markle’s parents Thomas Markle and Doria Ragland, who divorced when their daughter was six, for her hand in marriage before proposing.
“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,” they were quoted as saying.
Harry initially confirmed his relationship with the American actress in November last year in a statement from Kensington Palace attacking the media for subjecting his fiancée to a wave of abuse and harassment.
Markle is the daughter of an African-American mother and a father of Dutch and Irish descent.
Her father was a cinematographer when he met with her mother, who is a social worker and a yoga therapist.
Daily Mail reports that Thomas Markle was a divorcee with two children when he married Ragland. Meghan remains close to her mother, who divorced her father when she was just six years old.
The Prince of Wales has announced the engagement of Prince Harry and Ms. Meghan Markle. pic.twitter.com/rtlAnFCWTf
— Kensington Palace (@KensingtonRoyal) November 27, 2017
Additional reporting by Daily Mail