The BBC station has commissioned the hour-long episode, which will combine music and drama in a collaboration with the BBC's London Radio Drama team.
Shout to the Top will follow a three-piece all-female group in the beginning stages of their music careers in 1988.
The episode will show the group's formation, first gig, demo recording and turning down their first record contract.
Hannah Arterton, Fiona Macrae and Samantha Robinson will play The Velveteens, and will sing original songs alongside covers of bands from the late 1980s.
EastEnders actor Richie will play pub landlord Vince, the father of lead singer Rain. As an amateur singer, he becomes the group's manager.
The drama is written by The Farm's Roy Boulter and Sleeper's frontwoman Louise Wener. It is directed by Toby Swift, while music has been provided by Grammy Award-winning producer Brian Rawling and Mark Bates.
Jeff Smith, head of music for BBC Radio 2 and 6 Music, said: "Shout to the Top is a great original British drama for music radio. It is unique and distinctive and I don't think listeners will hear this kind of show on any other radio station.
"We have some of the best names in the business involved - including two very gifted writers who have come from a pop music background, namely Roy Boulter, formerly of The Farm, and Louise Wener from Sleeper.
"In addition to these fantastic names behind the scenes, we also have the amazing talent on air of Shane Richie and three very talented female leads who act and sing all the dialogue and songs. Considering they are all individual actors, it's incredible how quickly they became the 'band'."
Richie added: "It was a great honour and a wonderful opportunity to be asked to be part of this drama for Radio 2. The script is fantastic and I was surrounded by some wonderful new talent, which I am sure we will see more from in the future."
Shout to the Top will air on September 25 at 10pm on BBC Radio 2.