The Atomic Kitten star, who recently announced she was bankrupt for the second time, said she is "thrilled" to take centre stage as one of the world's most famous screen legends.
Writers say the musical, which is set to debut in the autumn, will be a "new route into the personal history of Marilyn based on little known facts from her life".
In an official statement, Kerry said: "I'm thrilled to have been given this opportunity to play one of the world's biggest female icons and can't wait to get to work.
"A successful career in drama has always been a main goal of mine and this role is a challenge but one I'm going to grab with both hands."
Kerry, who is engaged to George Kay, shared the news of her new job with fans on Twitter. This is the first acting role for the 32-year-old, who is known for her reality show appearances in I'm a Celebrity... Get Me Out of Here!, Celebrity Big Brother and Dancing On Ice.
Kerry also follows in the footsteps of her Atomic Kitten bandmate Natasha Hamilton, who landed a leading role in the smash-hit musical Rent last month.
Liberty X singer Michelle Heaton, who joined Kerry on ITV2 reality show The Big Reunion, tweeted: "Wow... Congrats honey! That's amazing xxx @KerryKatona7 xxx."
Norma Jeane: The Musical writer Belvedere Pashun, added: "Marilyn's life was one of extremes - poverty, abandonment, abuse followed by a flowering beauty which brought attention, fame, wealth and power and then the well documented tragic fall.
"I needed an actor of huge talent, personality and experience - Kerry was at the top of my list."
Kerry is still performing with her Atomic Kitten bandmates Natasha and Liz McLarnon, after they regrouped on The Big Reunion earlier this year. Last week (19 July) the trio belted out their pop hits to a 15,000-strong crowd at Summer Nights Live music concert in Durham.