The laser wake-field accelerator (LWFA) traditionally produces high brightness, quasi-monoenergetic electron beams with Gaussian-like spatial and angular distributions. In the present work we investigate the generation of ultra-relativistic beams with ring-like structures in the blowout regime of the LWFA using a dual stage accelerator. A density down-ramp triggers injection after the first stage and is used to produce ring-like electron spectra in the 300 - 600 MeV energy range. These well defined, annular beams are observed simultaneously with the on-axis, high energy electron beams, with a divergence of a few milliradians. The rings have quasi-monoenergetic energy spectra with an RMS spread estimated to be less than 5%. Particle-in-cell simulations confirm that off-axis injection provides the electrons with the initial transverse momentum necessary to undertake distinct betatron oscillations within the plasma bubble during their acceleration process.