We study the gravitational collapse of axion dark matter fluctuations in the postinflationary scenario, so-called axion miniclusters, with N-body simulations. Largely confirming theoretical expectations, overdensities begin to collapse in the radiation-dominated epoch and form an early distribution of miniclusters with masses up to 10^{-12} M_{⊙}. After matter-radiation equality, ongoing mergers give rise to a steep power-law distribution of minicluster halo masses. The density profiles of well-resolved halos are Navarro-Frenk-White-like to good approximation. The fraction of axion dark matter in these bound structures is ∼0.75 at redshift z=100.