The integrated computational materials engineering approach is inherently suited to explore the vast, multi-dimensional high entropy alloy (HEA) compositional and processing space, and has been adopted in this work, coupled with empiricism, to design highly corrosion resistant HEAs. Using the combination of empirical and computational approaches, three non-equimolar HEA compositions were identified for their predicted ability to form a single-phase structure and to exhibit high corrosion resistance. Phase diagrams and E-pH Pourbaix diagrams for HEAs were calculated by CALPHAD. One of the HEAs, Ni38Cr21Fe20Ru13Mo6W2, has been successfully synthesized on the lab-scale and homogenized at 1250°C for 120 hours. Exceedingly high corrosion resistance of the Ni-rich HEA was demonstrated by electrochemical testing, including potentiodynamic polarization and electrochemical impedance spectroscopy, even in harsh acidic solutions. The successful validation of the computational design efforts with pre-set property goals shows that ICME is suitable for corrosion resistant HEA design, including complex non-equimolar HEAs.