Dig a 12-inch deep hole near the agapanthus with a shovel. Fill the hole with water. If it takes longer than 12 hours to drain completely, you'll know you have a drainage problem.
Place a cubic yard each of peat, sand and organic garden soil in a nearby area. Mix it thoroughly with a spade, shovel, or your hands until you have a deep, rich mixture.
Dig out your agapanthus bulbs with a spade, and set them in a bucket of water to reduce shock while you amend the planting area.
Till the new soil into the poorly draining soil with a tilling machine, or using a shovel to turn, dig and mix. It is not necessary to cart away old soil. You're actually raising the planting area by about 12 inches.
Replant the agapanthus bulbs, spacing them 24 inches apart and covering them to the root crown of the bulb. Tamp the soil down firmly over side roots to eliminate air spaces that can dry them out.