The episode, called Shada, was described as "the greatest Doctor Who story never shown" and began filming in 1979 but production was halted by industrial action.
Following several false starts in attempting to bring it back, the drama will finally be premièred in a webcast on BBCi in the spring.
Paul McGann will star as the doctor, backed by a well-known cast including James Fox, Andrew Sachs, Hannah Gordon and Melvyn Hayes.
Director Nicholas Pegg hailed it as "a tremendously exciting project".
"We've really pulled out all the stops on this one," he said.
"We've had a fantastic time in the studio and I hope people will agree that we've done justice to one of the greatest writers Doctor Who was ever blessed with."
Shada, which was originally planned to conclude Dr Who's 17th season, finds the doctor teaming up with Romana (Lalla Ward) and K9 (John Leeson) in trying to track down the most dangerous book in the universe.
Produced by the Big Finish company, it stars Fox in the role of Professor Chronotis, with Sachs as the evil Skagra.
Gordon is behind the silky voice of Skagra's spaceship, and Hayes makes a cameo performance as college porter Wilkin.
McGann played the eighth doctor in the 1996 TV movie, seven years after the TV show was axed.
Other roles are played by Sean Biggerstaff - Quidditch captain Oliver Wood in the Harry Potter films - and Susannah Harker from political thriller House Of Cards.
'Tribute'
Producer Jason Haigh-Ellery was full of praise for Adams' writing.
"This is a great opportunity to finally produce Doctor Who's most famous lost script, and a fine tribute to Douglas Adams," he said.
Adams, who wrote the incredibly successful Hitchhiker's Guide To The Galaxy, died last year at the age of 49.