Magnetic reconnection is a fundamental plasma process involving an exchange of magnetic energy to plasma kinetic energy through changes in the magnetic field topology. In many astrophysical plasmas magnetic reconnection plays a key role in the release of large amounts of energy cite{hoshino1}, although making direct measurements is challenging in the case of high-energy astrophysical systems such as pulsar wind emissions cite{lyubarsky1}, gamma-ray bursts cite{thompson1}, and jets from active galactic nuclei cite{liu1}. Therefore, laboratory studies of magnetic reconnection provide an important platform for testing theories and characterising different regimes. Here we present experimental measurements as well as numerical modeling of relativistic magnetic reconnection driven by short-pulse, high-intensity lasers that produce relativistic plasma along with extremely strong magnetic fields. Evidence of magnetic reconnection was identified by the plasmas X-ray emission patterns, changes to the electron energy spectrum, and by measuring the time over which reconnection occurs. Accessing these relativistic conditions in the laboratory allows for further investigation that may provide insight into unresolved areas in space and astro-physics.