BIFROST, an upcoming instrument for the VLTI, is part of the Asgard Suite, a VLTI visitor instrument. It comprises two spectrograph arms that are optimised for wavelength range of 1- 1.75μm (fed by a fiber that is placed on-axis for fringe tracking/monitoring) and 1-1.3μm (fed by a fiber that can positioned either on-axis or off-axis to observe a faint target) wavelength range, respectively. Volume phase holographic gratings (VPHGs) are employed to achieve high spectral resolving power up to 25,000 and a throughput above 75% for all dispersing elements. In this contribution, we discuss the optical and optomechanical design of the spectrographs, as well as a new relay optics design that minimizes the thermal background, with a factor 4 reduction in thermal background compared to the non-relay optics design. We will also present the first lab results obtained with the YJH spectrograph.