"In many ways, pursuing a more compassionate and equitable world begins with these core values.
"Equally, to depict another side of masculinity - one grounded in connection, emotion, and softness - is to model a world that so many would like to see for their sons and daughters alike. Thank you for supporting me in this special project."
The book is currently number one on The New York Times Bestseller list for children's picture books, but failed to hit the UK Official Top 50 chart after selling 3212 copies in its first week.
Meghan - who has 2-year-old son Archie and newborn daughter Lilibet with 36-year-old Harry - recently revealed she would be distributing 2000 copies of the book to schools and libraries in her native US in a bid to "help nourish the community" by sending copies of the tale to various organisations.
In a joint statement the Sussexes said: "The Duchess and Archewell have received the support of the publisher of The Bench to distribute 2000 copies at no cost to libraries, community centres, schools, and non-profit programs across the country.
"Those receiving free copies include vital organisations like Assistance League of Los Angeles, which has served the local community for more than 100 years and which The Duke and Duchess visited twice last year to spend time with the children at the organisation's Preschool Learning Center.
"To make this happen, Archewell is working with the team at First Book, a non-profit social enterprise that's distributed more than 200 million books and educational resources to programs and schools serving kids in low-income communities in the United States and Canada. Reaching an average of 5 million kids per year, the First Book Network operates in classrooms, after-school programs, libraries, community programs, military support programs and more."