An apparatus for packaging products having different shape and dimensions, such as for example food products of different size, into pre-formed bags of appropriate size, such as for example heat-shrinkable bags of thermoplastic material, comprises a conveyor for carrying in sequence a plurality of products to be packaged from a product loading portion to a product packaging bracket end portion thereof, means for detecting the dimensions of each product to be packaged while it moves from said product loading portion to said product packaging bracket end portion of said at least one conveyor and a plurality of bag dispensing devices for dispensing a plurality of bags varying in at least one dimension thereof. The apparatus also comprises means for automatically selecting a bag dispensing device from said plurality of bags dispensing devices, depending on the detected product dimensions, and means for picking-up a bag from the selected bag dispensing device and positioning it around the product packaging bracket end portion of said at least one conveyor thus packaging the product present thereon. A method for packaging products by means of an apparatus of the type above described is also disclosed.