Select a planting location in full sun with soil that is friable, high in nitrogen and holds moisture well. To prevent legginess, amend the conditions that initially caused the problem. If light exposure was poor, plant the broccoli in a full-sun location. If high temperatures caused the spindly growth habit, a semi-shaded location may be preferred.
Dig a hole in the chosen planting spot that is a few inches deeper than the root system of the broccoli plant.
Dig around the root system of the broccoli plant, using care to avoid damaging the roots, and remove it carefully from the soil. Broccoli roots are somewhat shallow and fibrous, making transplanting a reasonable feat, as long as you do not expose the roots for too long.
Place the root system into the new hole so the stem is slightly deeper than where it was planted originally. This extra depth will help provide support to the spindly plant, which lacks the strength and sturdiness that it would normally have. Fill the hole with soil and pack it around the base of the plant to keep it upright.