To move multiple products, first make sure you are on the Product Management page. Navigate to the Settings drop-down menu. Select Products to get to the Product Manage page.
Select the products you wish to move.
Click the Tools button in the top left corner.
You'll see a menu drop down that will allow you to perform additional tasks. Under Move to Category, you'll see a list of your current existing categories. Click on the category you wish to move your products to.
Your products will now be in the appropriate category.