The as yet untitled book, which will be published next September, comes more than 90 years after Christie introduced Poirot in her first novel The Mysterious Affair at Styles.
Christie's grandson Mathew Prichard said: "It was pure serendipity that led to Sophie Hannah being commissioned to write this book.
"Her agent happened to approach HarperCollins in exactly the same week that my colleagues and I had started discussing a new Christie book. Her idea for a plot line was so compelling and her passion for my grandmother's work so strong, that we felt that the time was right for a new Christie to be written."
Hannah, whose psychological crime fiction is published in 24 countries, said Christie was the writer who made her "fall in love with mystery fiction" when she was 13.
She said: "I read and collected all her novels within a year, and have been a passionately - some might say obsessively - devoted fan ever since. It was Hercule Poirot and Miss Marple who, between them, made me want to devote my working life to crime fiction."