The Enhanced Resolution Imager and Spectrograph (ERIS) is a next-generation, adaptive optics assisted, near-IR imager and integral field spectrograph (IFS) for the Cassegrain focus of the Very Large Telescope (VLT) Unit Telescope 4. It will make use of the Adaptive Optics Facility (AOF), comprising the Deformable Secondary Mirror (DSM) and the UT4 Laser Guide Star Facility (4LGSF). It is a rather complex instrument, with its state of the art AO system and two science channels. It is also meant to be a "workhorse" instrument and offers many observation modes. ERIS is being built by a Consortium of European Institutes comprising MPE Garching (D), ATC (UK), ETH Zürich (CH), Leiden University (NL) and INAF (I) in collaboration with ESO. The instrument passed Final Design Review in mid-2017 and is now in the MAIT phase. In this paper we describe the design of the ERIS Instrument Software (INS), which is in charge of controlling all instrument functions and implementing observation, calibration and maintenance procedures. The complexity of the instrument is reflected in the architecture of its control software and the number of templates required for operations. After a brief overview of the Instrument, we describe the general architecture of the ERIS control network and software. We then discuss some of the most interesting aspects of ERIS INS, like the wavefront sensors function control, AO secondary loops, IFS quick-look processing and the on-line processing for high-contrast imaging observations. Finally, we provide some information about our development process, including software quality assurance activities.