Mix all the brine ingredients in a large container with a lid and add turkey legs. Let sit in brine for 12-24 hours, stirring occasionally.
Prepare charcoal grill for indirect cooking at about 325F. Meanwhile, remove turkey legs from brine, rinse and pat dry. Mix rub ingredients together in a small bowl (except the olive oil). Lightly drizzle olive oil over the turkey legs, then sprinkle all the rub over the legs and gently rub o coat.
Cook over indirect heat (325F) for 45 mins- 1 hour or until thickest part of leg is 165F. Turn legs every 10-15 minutes to cook evenly.