Pop 1 popcorn package at a time in the microwave on high until popping begins to slow down, about 2 1/2 minutes. Open bags carefully and transfer popcorn to a large plastic bag, discarding any burnt pieces or unpopped kernels.
Melt white chocolate chips with butter in top of a double boiler over simmering water, stirring frequently and scraping down the sides with a rubber spatula, until mixture is creamy, about 5 minutes.
Drizzle melted chocolate over popcorn. Close bag and shake until thoroughly coated, 3 to 4 minutes. Place in the refrigerator to cool, about 1 hour.