The Royal Mail said it had reached an agreement with Buckingham Palace to issue the stamps next year ahead of the prince's birthday on 21 June.
The company said it expected "enormous world-wide interest" in the 27p first-class stamps.
Details of the design are expected to worked out between the Royal Mail and palace officials over the coming months.
The Queen will have final approval, as with all royal commemorative stamps.
'Enormous interest'
Gavin Macrae, managing director of Royal Mail Stamps and Collectibles, said: "This will be the first time Royal Mail has issued a stamp to commemorate a royal `coming of age' and we are confident there will be enormous worldwide interest from the public and collectors alike.
"This Royal issue follows a long tradition of commemorative stamps produced to celebrate special events in the life of the Queen and immediate members of the Royal Family."
But it will not be the first time Prince William has appeared on British stamps.
The Prince, currently studying history of art at St Andrews University in Scotland, appeared in a special miniature stamp with the Queen Mother, the Queen and the Prince of Wales to celebrate the centenary of the birth of the Queen Mother on 4 August 2000.
St James's Palace declined to comment on the stamps.