An apparatus for dewatering dredge spoils includes a floating barge having a planar upper surface or deck. One end of the barge, such as the stern, is partially flooded or otherwise ballasted so that the deck slopes downwardly from the bow toward the stem. Dredge spoils removed from a waterway are deposited onto the bow where they flow down toward the stem. A plurality of concrete blocks on the deck form an attenuator that, in turn, defines one or more settling ponds on the surface of the barge. A weir across the stem of the barge forms an additional settling pond at the rear of the barge. Solids suspended in the water removed from the waterway settle out onto the deck when the dredge spoils are deposited onto the bow. Remaining solids suspended in the water deposit onto the deck as the water flows through the settling ponds. The relatively clear water that remains then flows back into the waterway off the stem of the sloped barge after passing through the settling ponds. Because the apparatus and method use materials and equipment, such as the barge and blocks, that are already likely to be on hand, the method and apparatus are particularly economical and easy to implement.