  Magnetic reconnection is a fundamental plasma process associated with
conversion of the embedded magnetic field energy into kinetic and thermal
plasma energy, via bulk acceleration and Ohmic dissipation. In many high-energy
astrophysical events, magnetic reconnection is invoked to explain the
non-thermal signatures. However, the processes by which field energy is
transferred to the plasma to power the observed emission are still not properly
understood. Here, via 3D particle-in-cell simulations of a readily available
(TW-mJ-class) laser interacting with a micro-scale plasma slab, we show that
when the electron beams excited on both sides of the slab approach the end of
the plasma structure, ultrafast relativistic magnetic reconnection occurs in a
magnetically-dominated (low-$\beta$) plasma. The resulting efficient particle
acceleration leads to the emission of relativistic electron jets with cut-off
energy $\sim$ 12 MeV. The proposed scenario can significantly improve
understanding of fundamental questions such as reconnection rate, field
dissipation and particle acceleration in relativistic magnetic reconnection.
