On December 10, 1936, King Edward VIII submitted his abdication and it was endorsed by Parliament the next day. He thus became the only British monarch ever to resign voluntarily.
The speech below is from December 11, when Edward publicly announced his decision via radio to a worldwide audience. http://www.historyplace.com/speeches/edward.htm
His younger brother, George VI, took the throne on May 12, 1937
and immediately gave Edward the title, Duke of Windsor.
The Duke and Simpson were married in France on June 3, 1937. The new Duchess of Windsor wore this Mainbocher gown, now one of the most identifiable fashion items in history. The gown now resides in the Costume Collection of the Metropolitan Museum of Art in New York. http://www.metmuseum.org/Works_Of_Art/viewOne.asp?dep=8&viewmode=0&item=C.I.50.110a–l