The 35-year-old former Destiny's Child member and 30-year-old singer will play Warwick and Cilla Black, respectively. Warwick, 75, announced the project at the 2016 Cannes International Film Festival on Friday.
Dionne is based on Warwick's autobiography, My Life As I See It, which was released in 2010. Actor and New Jack City director Mario Van Peebles is in talks to direct, with filming to begin in October.
"This is my 57th year in this business, and I have been asked, 'When are you gonna let us know about this? Tell us about that?' So it's finally at the point where instead of what you think you know about Dionne Warwick, now you will know," Warwick said.
Warwick is the second most-charted female vocalist of all time and has sold over 100 million records in her career. The film will take place in the 1960s and co-star Danny Glover as Warwick's father and Olympia Dukakis as Marlene Dietrich.
Dionne will cover Warwick's feud with Black, which started after Black released a successful version of Warwick's song "Anyone Who Had a Heart." Warwick said the movie will explain why Black, who died in August, became her "nemesis."
Luckett is best known as a founding member of Destiny's Child and appeared on two albums with the girl group. She will release her third solo album, Until Then, this year, and last starred in the comedy Lucky Girl with Columbus Short.
Lady Gaga, meanwhile, is working on her fifth studio album. The singer made her major television debut on FX series American Horror Story: Hotel and is expected to return for the show's sixth season.