HarperCollins Publishers said the Queen has personally given her in-house designer her blessing to tell the story of their "unparalleled bond".
She is the first serving member of the Royal Household to receive such permission, the publishers said.
The book will include never-seen-before photos of The Queen from Ms Kelly’s private collection over the last 25 years of working together
ITV News Royal Editor Chris Ship tweeted: "The publisher Harper Collins says Angela Kelly’s book will be ‘revealing’ and will give ‘memorable insights into what it’s like to work so closely with The Queen’."
A spokeswoman for HarperCollins said: "The Queen has personally given Angela her blessing to share their unparalleled bond with the world.
"Angela Kelly is the first serving member of the Royal Household to have been given this extraordinary permission.
"Whether it’s preparing for a formal occasion or brightening Her Majesty’s day with a playful joke, Angela’s priority is to serve and support."
The publisher added: "Sharing never-before-seen photographs - many from Angela’s own private collection - and charming anecdotes of their time spent together, this revealing book provides memorable insights into what it’s like to work closely with The Queen, to curate her wardrobe and to discover a true and lasting connection along the way."
Entitled The Other Side Of The Coin: The Queen, The Dresser And The Wardrobe, the book will be published on October 29.
Ms Kelly, who is the daughter of a Liverpool dockworker, has worked with the Queen for 25 years.
Her full title is Her Majesty’s Personal Adviser and Curator (The Queen’s Jewellery, Insignias and Wardrobe), Senior Dresser and In-house Designer.
Ms Kelly, who started in the Royal Household in 1994 as assistant dresser, has also become the Queen’s confidante and is seen as her "gatekeeper".
She rarely gives interviews but once disclosed: "We are two typical women. We discuss clothes, make-up, jewellery."
The Queen values the opinion of her meticulous personal assistant and has gradually over the years given Ms Kelly free rein when helping her create a look for an event.
Ms Kelly is credited with keeping the Queen’s style relevant, and for adding a "touch of bling".
Despite the Queen’s advancing years she has been prepared to embellish her style, under Ms Kelly’s direction, as a nod to modern times.
A pair of 3D glasses worn by the Queen during a film demonstration in Canada in 2010 were given a touch of glamour by Ms Kelly - Swarovski crystals forming the letter Q on their sides.
Samantha Cohen, who was assistant private secretary to the Queen for seven years and is the Duke and Duchess of Sussex’s outgoing private secretary, said: "This book documents the unique working relationship between Her Majesty The Queen and the woman who has been her personal adviser and senior dresser for more than two decades: Angela Kelly.
"It gives a rare glimpse into the demands of the job of supporting the monarch, and we gain privileged insight into a successful working relationship, characterised by humour, creativity, hard work, and a mutual commitment to service and duty."
In 2012, Ms Kelly wrote Dressing The Queen which celebrated The Queen’s Diamond Jubilee.