A laser-based emittance monitor has been developed to non-invasively measure the transverse emittance of the LINAC4 H− beam at its top energy of 160MeV. After testing several sub-systems of the instrument during linac commissioning at intermediate energies, two instruments are now permanently installed. These instruments use a pulsed laser beam delivered to the accelerator tunnel by optical fibres before final focusing onto the H− beam. The photons in the laser pulse detach electrons from the H− ions, which can then be deflected into an electron multiplier. In addition, the resulting neutral H0 atoms can be separated from the main beam by a dipole magnet before being recorded by downstream diamond strip-detectors. By scanning the laser in the horizontal and vertical plane the beam profiles are obtained from the electron signals and the emittance can be reconstructed by the H0 profiles at the diamond detectors. This paper describes the final system layout that consists of two independent instruments, each measuring profile and emittance of the H− beam in the horizontal and vertical plane and discusses the preliminary commissioning results.