A new cultivar of Agapanthus, ‘AMPU001’, that is characterized by its fast growing and fast multiplying growth habit, a compact plant habit, inflorescences that form dense umbels of flowers that are dark violet-purple in color, an extended flowering season blooming and re-blooming from early spring to late summer and sporadically in early fall, a very floriferous blooming period producing an unusually high number of inflorescences, and its good resistance to fungal infection from Macrophoma agapanthii.