The adaptation of Piper Kerman's 2011 book will be released exclusively by the online provider as part of a new range of original programming.
Taylor Schilling (The Lucky One) will play the lead role in the drama, which tells the true story of Kerman, who was sentenced to 15 months in a notorious Connecticut prison after becoming involved in the drug trade.
Mulgrew has signed up to play Red, a Russian woman who runs the prison kitchen and serves as a mother figure for her fellow inmates, according to Deadline.
The 57-year-old actress is best known for her role as Captain Kathryn Janeway on Star Trek: Voyager and currently plays a recurring role on Syfy's Warehouse 13.
That '70s Show star Laura Prepon will also appear in Orange Is the New Black as Kerman's ex-girlfriend, drug runner Alex.
Jason Biggs (American Pie) is another cast member for the 13-part series, which is being adapted for television by Weeds creator Jenji Kohan.
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