Soil weighs 75 to 100 pounds per cubic foot, which means a single 4 by 8 foot bed filled a foot deep holds around 2,400 to 3,200 pounds of dirt. In almost every case it makes more financial sense to rebuild the beds and buy fresh soil than to move either one.
Pro tip: Photograph the bed layout and spacing in your current garden before demolition, since sun exposure and drainage that took a season to figure out is easy to forget.
Watch out: A filled 4 by 8 foot bed can hold well over a ton of soil; never attempt to lift or drag a full bed, always empty it first.