The drama will show a young Eric Bartholomew as a reluctant performer who has a chance meeting with precocious child star Ernie Wiseman.
The pair strike up an unlikely friendship on the children's variety circuit.
Eric, encouraged by mother Sadie, becomes the funnyman to Ernie as the pair struggle to break into the big time before becoming one of Britain's most successful comedy duos.
The story, whose title is yet to be decided, was penned by Peter Bowker, whose credits include Desperate Romantics and Occupation.
The channel's new line-up will also see new Doctor Who star Matt Smith regenerate into writer Christopher Isherwood in a 90-minute film.
Christopher And His Kind, based on Isherwood's 1976 memoir of the same name, also stars Lindsay Duncan who recently appeared in Doctor Who with David Tennant.
Duncan, who also recently portrayed Baroness Thatcher for BBC Two, plays Isherwood's mother, with whom the writer has a "suffocating relationship".
The Crimson Petal And The White, a "sexually charged" tale taking viewers into the murky world of Victorian prostitution, is also being turned into a four-part series for the channel as part of its new raft of homegrown drama.
Speaking at a Broadcasting Press Guild meeting in London, BBC Two controller Janice Hadlow said: "Strongly authored dramas, whether adaptation or original writing, are absolutely key to the creation of BBC Two's confident new voice."