The new and distinct cultivar of ornamental Japanese Anemone plant named Anemone ‘;Sweetly’; with medium spreading habit, dense vertical peduncle of numerous semi-double flowers with deep rose-pink petals, beginning late summer and continuing into early fall, set just above the dark green, tri-foliate leaves with irregularly serrated to biserrated margins. The new plant is useful for landscaping as a specimen, en masse, or in containers.