Preheat the oven to 350°F (175°C). Grease and flour a 9×5 inch loaf pan or line it with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg until well combined.
In a large bowl, beat the granulated sugar, light brown sugar, and eggs together until smooth and creamy.
Add the vegetable oil, Greek yogurt, and vanilla extract to the sugar and egg mixture. Mix until fully incorporated.
Fold the dry ingredients into the wet ingredients gently until just combined. Do not overmix.
Fold in the grated zucchini until evenly distributed throughout the batter.
Pour the batter into the prepared loaf pan and spread it evenly.
Bake in the preheated oven for 55 to 60 minutes, or until a toothpick inserted into the center comes out clean.
Remove the bread from the oven and let it cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely before slicing.