Who wrote the story of the monkey king?

No....and yes

The Monkey King stories which we hear today are based on the classic Chinese novel Journey to the West, published in the 1590s, which in turn is based on traditional tales about Sun Wukong - the Monkey King, and Great Tang Records on the Western Regions by the Buddhist monk Xuanzang.

Xuanzang was a real person who travelled from China to India in 629-645 AD in search of knowledge and Buddhist scriptures. On his return to China he wrote about his travels and the things he saw and the people he met. He became very famous in China and made an important contribution both to Chinese culture and the Buddhist religion.

His story is reflected in the adventures of Tripitaka, the monk from the Monkey stories, who Monkey, Pigsy and Sandy have to help on his quest to India to find Buddhist scriptures.

Unfortunately for Xuanzang, the parts of the story about the immortal assistants was a later, fictional addition.