Coel, 36, shot to fame with her Channel 4 comedy Chewing Gum, which was based on her 2012 play of the same name.
The TV series, which aired three years later, earned Coel two Bafta TV Awards for best breakthrough talent and best female comedy performance.
Her next series, I May Destroy You was even more successful, winning a plethora of awards including an Emmy and five Baftas.
She has previously spoken about rejecting $1m (£730,000) from Netflix for the series because the BBC offered her more creative control.
Since then, she has appeared in Marvel’s Black Panther: Wakanda Forever and Amazon TV series Mr & Mrs Smith.
US network HBO will co-produce First Day On Earth, which will be made by production company Various Artists Limited in association with film studio A24.
