Ariana will play Galinda, while Oscar-nominated British actress Cynthia will appear as Elphaba.
Jon M Chu, the filmmaker known for Crazy Rich Asians and In The Heights, is on directing duties for the big screen version of the record-breaking musical.
Cynthia shared a picture showing the moment she found out about the role on Instagram, alongside a handwritten message from Grande.
It said: “Dear Cynthia, honoured doesn’t even begin to cover it. I cannot wait to hug you. See you in Oz. All my love, Ari.”
The US singer also posted a picture of the moment she was told about the role with her 237 million Instagram followers.
Cynthia’s message to her said: “Congratulations Miss A, the part was made for you, I look forward to sharing this musical journey with you. Love, Cynthia.”
Jon M Chu wrote: “These two witches!! The emotional moment I got to tell @cynthiaerivo and @arianagrande that they were our Elphaba and Galinda in the @WickedMovie for @unistudios wait until you see what they bring!! It is other worldly. Ahhhhh!!!”
Wicked tells the backstory of The Wizard of Oz and what happened before Dorothy arrived in the enchanted world.
It debuted on Broadway in 2003 and has since surpassed one billion dollars (£742 million) in revenue – only the third show to do so alongside The Phantom Of The Opera and The Lion King.
As well as being of the world’s biggest pop stars, Ariana also has an acting background. She will appear in Adam McKay’s star-studded black comedy Don’t Look Up later this year.
Cynthia, a Londoner, is accomplished on both the stage and screen. She has won an Emmy, a Grammy and a Tony Award, as well as earning a best actress nomination at the Oscars for 2019 biopic Harriet.