In a small saucepan over low heat, stir gelatin into boiling water and stir until dissolved. Remove from heat.
Add strawberries, corn syrup and vanilla and stir until strawberries are completely thawed. Transfer to a blender container. Cover and blend until pureed.
Place yogurt in a medium bowl. Whisk in strawberry mixture until well blended. Pour into eight 5-ounce paper cups. Insert a popsicle stick in center of each. Freeze for 3 to 4 hours, wrapping in foil or placing in plastic bags after mixture is firm.