KMOS is a second generation instrument in construction for use at the European Southern Observatory (ESO) Very Large Telescope (VLT). It operates in the near-infrared (0.8 to 2.5 microns) and employs 24 deployable, image slicing integral field units (IFUs) feeding three spectrographs. The spectrographs are designed and built by a partnership of the University of Oxford and Rutherford Appleton Laboratories (RAL). We describe the assembly, integration and alignment procedures involved in the construction of these spectrographs in detail. We also present the results of the cryogenic optical tests, including the first data taken through the full spectrograph optical train and the details of the test facility and procedures involved.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.