The actress chosen is Jemma Powell, who played Jacqueline Hill in 2013's An Adventure In Space and Time, the Mark Gatiss-helmed documentary about the origins of the show.
Powell said of the announcement:
A huge honour to be reviving Barbara after portraying her in An Adventure in Space and Time. Thankyou for having me @bigfinish #doctorwho[Source: Kasterborous]
— Jemma Powell (@jemmapowell01) September 13, 2014