Episodes will follow the cast as they try and conduct rehearsals – with dysfunctional results.
Tennant and Sheen previously acted together in last year’s Amazon Prime adaptation of Terry Prattchet and Neil Gaiman’s novel Good Omens.
The pair will be joined by as-yet-unnamed guest stars across the series. The confirmed supporting cast includes Tennant’s wife, Georgia Tennant (Merlin), Lucy Eaton and Anna Lundberg.
Each episode will last just 15 minutes; the entire series will be added to BBC iPlayer in June.
BBC’s director of content Charlotte Moore said: “It’s so important that the BBC provides moments of humour and light relief.
She added: “This mischievous idea shows what great sports Michael and David are.”