Magnetic reconnection is a process that changes magnetic field topology in highly conducting fluids. Within the standard Sweet-Parker model, this process would be too slow to explain observations (e.g. solar flares). In reality, the process must be ubiquitous as astrophysical fluids are magnetized and motions of fluid elements necessarily entail crossing of magnetic frozen in field lines and magnetic reconnection. In the presence of turbulence, the reconnection is independent of microscopic plasma properties, and may be much faster than previously thought, as proposed in and tested in Kowal et al. (2009Kowal et al. ( , 2012. However, the considered turbulence in the LazarianVishniac model was imposed externally. In this work we consider reconnection-driven magnetized turbulence in realistic three-dimensional geometry initiated by stochastic noise. We demonstrate through numerical simulations that the stochastic reconnection is able to self-generate turbulence through interactions between the reconnection outflows. We analyze the statistical properties of velocity fluctuations using power spectra and anisotropy scaling in the local reference frame, which demonstrates that the reconnection produces Kolmogorov-like turbulence, compatible with Goldreich & Sridhar (1995) model. Anisotropy statistics are, however, strongly affected by the dynamics of flows generated by reconnection process. Once the broad turbulent region is formed, the typical anisotropy scaling l ∝ l 2/3 ⊥ is formed, especially for high resolution models, were the broader range of scales is available. The decay of reconnection outflows to turbulent-like fluctuations, characterized by different anisotropy scalings, strongly depends on β plasma parameter. Moreover, the estimated reconnection rates are weakly dependent on the model resolution, suggesting that no external processes are required to make reconnection fast.