"What Pet Should I Get?" was discovered in November 2013 while the author's widow, Audrey Geisel, was going through boxes of old material in their California home.
Publishers said it is expected to be followed by least two other books based on material left by the prolific and award-winning author Theodor Geisel, who wrote under the pen-name Dr. Seuss and who died in 1991.
"This book is all his drawings," the Geisels' former secretary, Claudia Prescott, said.
"It's the only (book) we found that was complete - some of the verses had slipped off the story boards because the scotch tape was so old it turned brown, so the Random House people went through and spent a lot of time getting them in the right order."
"What Pet Should I Get?" is published by Random House Children's Books, a unit of Germany-based media group Bertelsmann SE & Co KGaA.
Prescott, who has worked for the Geisels since 1972, said the author had many unfinished ideas, not all of which resulted in books.
"He called it the bone pile - he'd go and take something out of the bone pile," she said.
Cathy Goldsmith, the author's former art director, has said "What Pet Should I Get?" was probably written between 1958 and 1962.
It features the brother and sister characters introduced in the Dr. Seuss book "One Fish Two Fish Red Fish Blue Fish," which was published in 1960, and centers on their trip to a pet store to pick out a new friend.
Geisel, who began publishing books as Dr. Seuss in 1931, wrote and illustrated more than 45 books, including "The Cat in the Hat," "Green Eggs and Ham" and "How the Grinch Stole Christmas," before his death at the age of 87.
More than 650 million copies of his works have been sold worldwide.
Three other books have been published since Geisel died, but this is only the second where all the work was done by Geisel - except colouring the characters, which was done by Goldsmith.
