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Should you hope to take your gardens to the new place, ask the movers their policies on moving plants. Some will flat out refuse, most will simply state that they aren't responsible to keep the plants alive. Dig up your gardens in advance of the move, if the ground outside your housing unit isn't completely frozen. To prevent the plants from too much damage, re-plant them in commercial sized ice cream buckets. Make sure you take a good amount of soil with the plants, then water immediately after replanting. When the last few items are being stuffed into the moving truck, water the plants again, then slide clear lawn bags over the plants, tying them tightly at the top. Then place the bagged planters gently in tall boxes (5cu are best, so make sure the movers have a few extras set aside for you), cramming as many in as possible so they don't slide around, and write "THIS SIDE UP" on the box. Immediately before the movers are ready to close the truck, have the plants, in their respective boxes, lined up and ready to go.
*NOTE: Most movers are botanically-challenged, so ensure you label the buckets containing your "recreational" plants well in advance. "TOMATOES" is generally an acceptable substitute.