Marsh will portray Tanner in the 1960s with Prenger taking on 1980's Elsie in the show which, having recently been postponed, will now debut at Manchester Arena on 9 and 10 May 2012 before touring to Dublin, Belfast and Newcastle.
Paul O'Grady will also play a central role in the production, narrating proceedings which will track the "momentous events in Corrie's history".
Speaking about the role Marsh said in a press statement: “The strong, determined and indomitable women have always defined Coronation Street right from the very first episode to the present day and Elsie Tanner will go down in history as one of the most gossiped about women in Weatherfield.
"She’s left some rather big stiletto shoes to fill but to have the opportunity to represent such an iconic character of yesteryear on a stage of this scale is an absolute honour."
BAFTA winning film and stage director John Stephenson will direct the the show, which will feature a 25-piece orchestra, a “West End cast” and choreography from Olivier award winners Stephen Mear and Karen Bruce.
Co-scripted by Damon Rochefort, Street of Dreams will be executive produced by Kieran Roberts for ITV Studios and John Ward for Reckless Entertainment.
Paul O’Grady said: “I’m a great fan of the street, I’ve watched it for most of my life. Chunks of script from 30 years ago are engraved in my memory so to relive it all alongside unforgettable characters and talent on the stage, revisiting such iconic scenes from across the years, is just brilliant. I can’t wait to watch it all come together and the reaction it receives.”