The show, in which impressionists spoof figures from President George Bush to TV antiques expert David Dickinson, will attempt to become the latest in a long line of BBC radio comedies that have gone on to TV success.
A pilot episode, shown in March, was received "very, very well", according to the BBC, although some critics said the visual impressions were not as accurate as the aural ones that had won a dedicated radio audience.
The BBC Radio 4 show has picked up six major awards since starting in 2000, and the TV version will be shown on BBC Two from the autumn.
The pilot included items like BBC director general Greg Dyke hanging out of a BBC One hot air balloon, and an impression of Russell Crowe in Gladiator.
"My name is Maximus Decimus Meridius," began comic Jon Culshaw as Crowe in the opening sketch.
"Father to a murdered son, husband to a murdered wife - and that's when I called Claims Direct."
It is not known whether any more actors will be recruited to work with the radio team of Jon Culshaw, Jan Ravens, Mark Perry and Kevin Connolly.
Producers would meet in the next week to discuss what the show would look like.
"Dead Ringers will soon be a full time job and we're all up for it," Culshaw said.
"There's a lot of fleshing out of the characters to bring them to TV and we're looking forward to doing more of that."
Freedom
Producer Bill Dare said BBC Two and Radio 4 audiences had quite similar tastes, but there would be some characters who would not work as well on TV.
"Radio writers nearly always write great TV because they are used to the freedom that radio provides - and this makes their writing particularly visual," he said.
Another radio series is also being made.
Dead Ringers could follow the likes of The Hitchhiker's Guide To The Galaxy, The League of Gentlemen, Chris Morris, Alan Partridge and Harry Hill from the airwaves to screen success.