Tennant was the 10th actor to play the show's title character. Piper played his on-screen companion, Rose Tyler.
Filming of the special will begin next week, the BBC said. The 3-D show is due to air Nov. 23, 50 years to the date after the first episode, "An Unearthly Child," was broadcast.
Tennant's successor, Matt Smith, along with Jenna-Louise Coleman as Rose Tyler, will star in the special.
John Hurt will make an appearance, the BBC said.
The first episode of the 2013 season, "The Bells of Saint John," aired Sunday.