“When my soul fainted within me, I remembered the LORD. My prayer came in to you, into your holy temple. Those who regard vain idols forsake their own mercy. But I will sacrifice to you with the voice of thanksgiving. I will pay that which I have vowed. Salvation belongs to the LORD.” Then the LORD spoke to the fish, and it vomited out Jonah on the dry land.
Traditional attribution
The book names Jonah as its subject, not its author. Attribution to Jonah is traditional.