The 27-year-old, who was born in Las Palmas, returns to Spanish football after being released by Paris Saint-Germain.
This will be the second time Jese will have worn the colours of his local team, having made 16 appearances and scored three goals for Las Palmas while on loan from PSG in the second half of the 2016/17 season.
The forward was taking a medical on Tuesday and will be presented at the Estadio Gran Canaria on Wednesday.
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