Acrosome is formed during spermiogenesis.
Spermiogenesis is the final stage of spermatogenesis, which sees the maturation of spermatids into mature, motile spermatozoa.The process of spermiogenesis is traditionally divided into four stages: the Golgi phase, the cap phase, formation of tail, and the maturation stage.
At the cap/acrosome phase the Golgi apparatus surrounds the condensed nucleus, becoming the acrosomal cap.