Among the recovered 1960s footage is most of the classic story "The Web of Fear", a black and white adventure in which the Time Lord, then played by Patrick Troughton, battles a robot yeti in London's underground train system.
The tapes were found gathering dust in a television station in Jos, a central Nigerian city plagued by chronic sectarian violence.
The trove, which is being described by the BBC as the "largest haul of missing episodes recovered in the last three decades", also includes six-part story "The Enemy of the World."
"It's thrilling," said Mark Gatiss, author of recent "Doctor Who" episodes.
"Every single avenue seemed to have been exhausted, every now and then something turns up — but to have two virtually complete stories out of the blue is absolutely incredible."
The BBC destroyed many of the drama's original tapes in the 1960s and 1970s but some were copied for sale to foreign broadcasters.
Despite the find, 97 episodes remain lost.
The episodes were uncovered by Phillip Morris, director of Television International Enterprises Archive.
"The tapes had been left gathering dust in a storeroom at a television relay station in Nigeria," he told the BBC, adding that they were "just sitting on the shelf."
"I remember wiping the dust off the masking tape on the canisters and my heart missed a beat as I saw the words, Doctor Who. When I read the story code I realised I'd found something pretty special," he added.
The tapes originally went from Britain to Hong Kong and then on to a series of television stations in Nigeria as part of the distribution systems that operated at the time.
Morris said he had been "lucky" to find the tapes intact given the high temperatures in Nigeria.
"Fortunately in this case they had been kept in the optimum condition," he said.
He joked that he is often described as the "Indiana Jones of the film world" for discovering the cache of tapes.
Jos is the capital of Nigeria's Plateau state, in Nigeria's so-called "Middle Belt" where the mainly Christian south meets the majority Muslim north, and has been the site of waves of sectarian and ethnic violence in recent years.
The area has also been attacked by the Islamist group Boko Haram.
Morris added that it was "probably the largest haul of missing episodes recovered in the last 25, 30 years."
The new programmes will be available on iTunes from today and will be released on DVD later.
Fiona Eastwood, director of consumer products, BBC Worldwide, said: "We are thrilled with the recent discovery of The Web Of Fear and The Enemy Of The World and we're very happy to be launching re-mastered versions of these treasured episodes to fans as we celebrate the 50th year of Doctor Who."
The adventures of Doctor Who — a time travelling, humanoid alien who traverses the universe in Tardis spacecraft — have maintained a loyal following since they were first aired in 1963.
Scottish actor Peter Capaldi, best known as the abusive spin doctor in the political satire "The Thick of It", was named in August as the 12th actor to play the role.