An Adventure in Space and Time - which will tell the story of the BBC sci-fi drama's early days - has been written by Shearsmith's League of Gentlemen co-star Mark Gatiss.
"I first asked Reece [to play this role] about 12 years ago when I started thinking about this project," Gatiss told the Radio Times. "We were in the midst of League of Gentlemen and I just remember thinking, if anyone plays Patrick Troughton, it should be Reece.
"Like the second Doctor, he's small, saturnine and a comic genius. The complete package. He thought it was a fantastic idea and I've kind of nurtured it all this time."
Troughton played the second Doctor between 1966 and 1969, inheriting the show's lead role from original star William Hartnell, who will be played by Harry Potter's David Bradley in the biopic.
"Reece [is] not steeped in Doctor Who like I am,