On the morning of Friday, April 29, Her Majesty Queen Elizabeth II announced that she "has been pleased today to confer a Dukedom on Prince William of Wales". The prince is now His Royal Highness the Duke of Cambridge, Earl of Strathearn and Baron Carrickfergus. The announcement took place on the morning of Prince William's wedding to Miss Catherine Middleton; traditionally, royal princes in the past have received ducal titles from the monarch upon their marriages.
Miss Catherine Middleton thus becomes Her Royal Highness the Duchess of Cambridge after the wedding. Her official title in full, however, is Her Royal Highness Princess William Arthur Philip Louis, Duchess of Cambridge, Countess of Strathearn and Baroness Carrickfergus.
When Prince Charles, Prince of Wales succeeds to the throne as expected, the Duke and Duchess of Cambridge will automatically become the Duke and Duchess of Cornwall, the traditional title for the heir apparent. The title Prince of Wales is not automatically inherited and must be granted by the sovereign; therefore the Duke and Duchess of Cambridge will become the Prince and Princess of Wales at the will of the sovereign.
When the Duke of Cambridge succeeds to the throne, he would be styled as His Majesty King William V (should he choose his first name to be his regnal name) or simply His Majesty The King, and the Duchess of Cambridge will become Her Majesty Queen Catherine, or simply Her Majesty The Queen.