Prince William, the second in line to the British throne, will marry his long-term girlfriend Kate Middleton next year.
Prince William, 28, is the eldest son of heir to the throne, Prince Charles, and the late Princess Diana.
The £36,000 blue sapphire and diamond engagement ring is the one given by Prince Charles to Diana in 1981.
Prince William and Miss Middleton, both aged 28, became engaged in October while on holiday in Kenya. Miss Middleton is six months older than William.
They began dating while studying at Saint Andrews University in Fife.
The royal engagement was announced in a brief statement issued by Clarence House, which says they will marry in London in spring or summer next year.
Following the marriage, the couple will live in north Wales, where Prince William will continue to serve with the Royal Air Force as a search and rescue pilot.
The statement continued: "Prince William has informed the Queen and other close members of his family.
"Prince William has also sought the permission of Miss Middleton's father."
Prince Charles said he was "thrilled, obviously", joking: "They've been practising long enough."
The Queen said she was "absolutely delighted" for both Prince William and Miss Middleton.
The two graduated in the same ceremony from St Andrews in 2005 and their families joined them for a celebratory lunch.
Their relationship was exposed in 2005 when they were photographed together on the Swiss ski slopes of Klosters. They split briefly in 2007.
Miss Middleton's father, Michael, says they are overwhelmed by the news.