I am Tama, Lucky Cat: A Japanese Legend by Wendy Henrichs illustrated by Yoshiko Jaeggi

Bookseller blurb: Under the shadow of the white-capped mountains of Japan, a kind and gentle monk takes in a white cat with unusual markings and names him Tama, Lucky Cat. Tama watches as his new master teaches Buddha's ways to poor farmers, caring for their welfare while ignoring his own empty stomach. Tama truly earns his nickname -- "Lucky Cat," when during a powerful thunderstorm, he sees a towering warlord on a white horse. The cat beckons the warrior forward just as a large branch crashes to the ground and lands right where the warlord had previously stood. In gratitude to Tama, the warlord lavishes gifts on the monk's poor temple.

Here is the website for Yoshiko Jaeggi. You can see inside I am Tama, Lucky Cat here. 

You see these little waving cats in Asian restaurants and shops but I never thought to wonder about the story connection. Many years ago our school welcomed a delegation of educators from China. I immediately thought of the waving cat and I involved the children in making or colouring them for our library foyer notice board BUT just days before the visit I discovered the waving cat is a from Japan. I quickly had to pull down the display and make some sweet little purple origami pandas.  The visit went well (no one was offended by my error) although this visit was strange. It was all part of a proposal from the school Principal to partner with a school in China - this idea never eventuated.

Wikipedia tells me: Because of its popularity in Chinese communities (including Chinatowns) the maneki-neko is frequently mistaken for being Chinese in origin rather than Japanese, and is therefore sometimes referred to as a "Chinese lucky cat" or jīnmāo ("golden cat"). ... The figurines are often displayed in shops, restaurants, pachinko parlors, dry cleaners, laundromats, bars, casinos, hotels, nightclubs, and other businesses, generally near the entrance,[1] as well as households.[2] Some maneki-neko are equipped with a mechanical paw which slowly moves back and forth.

I found a couple of other books that explore this story - there are four different versions of the folktale from Japan (check the Wikipedia link above).