Place the popped popcorn in a very large mixing bowl. Remove any unpopped kernels.
In a medium saucepan, combine the sugar, light corn syrup, water, butter, and salt.
Cook over medium heat, stirring constantly, until the butter is melted and the sugar is dissolved.
Attach a candy thermometer to the pan and bring the mixture to a boil. Cook without stirring until the temperature reaches 250°F (hard-ball stage).
Remove the saucepan from the heat and carefully stir in the vanilla extract.
Slowly pour the hot syrup over the popcorn while tossing gently with a heatproof spatula to coat evenly.
Allow the mixture to cool just until it is safe to handle. Grease your hands with butter or non-stick cooking spray.
Firmly press the coated popcorn into 2 to 3-inch balls and place them on a sheet of wax paper or parchment paper to cool and set completely.
Notes
Store the popcorn balls in an airtight container at room temperature for up to 5 days. You can also wrap them individually in plastic wrap for easy sharing or gifting.