Cut the celery root, carrots, parsnips, and sweet potato into 1-inch pieces. (If the parsnips are very thick, cut them lengthwise in half and remove the hard core before cutting into pieces). Bring a large pot of water to a boil. Add the celery root, carrots, and parsnips. After 2 minutes, add the sweet potato and cook until the vegetables are partially cooked, 6 to 8 minutes more. Drain well.
Prepare the grill for direct cooking over medium heat (350° to 450°F) and preheat a perforated grill pan for about 10 minutes.
In a large bowl whisk the oil, rosemary, garlic, salt, and pepper. Add the vegetables to the bowl and turn to coat.
Spread the vegetables in a single layer on the grill pan and grill over direct medium heat, with the lid closed, until lightly charred and quite tender, about 10 minutes, turning occasionally. Serve warm.