The Eagles have picked up just seven points from 12 league matches since the start of December, their latest setback a 3-0 home defeat to leaders PSV on Saturday.
That result left Booy's men 15th in the table, a point above the relegation play-off zone.
And Booy has now confirmed he will move on, telling the club's official website: "I've made my choice. I'm ready for a change and that feeling I want to follow.
"The club deserves that I provide clarity."
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