Euclid is an ESA Cosmic Vision wide-field space mission concept dedicated to the high-precision study of Dark Energy and Dark Matter. The mission relies on two primary cosmological probes: Weak gravitational Lensing (WL) and Baryon Acoustic Oscillations (BAO). The first probe requires the measurement of the shape and photometric redshifts of distant galaxies. The second probe is based on the 3-dimensional distribution of galaxies through spectroscopic redshifts. Additional cosmological probes are also used and include cluster counts, redshift space distortions, the integrated Sachs-Wolfe effect (ISW) and galaxy clustering, which can all be derived from a combination of imaging and spectroscopy. Euclid Imaging Channels Instrument of the Euclid mission is designed to study the weak gravitational lensing cosmological probe. The combined Visible and Near InfraRed imaging channels form the basis of the weak lensing measurements. The VIS channel provides high-precision galaxy shape measurements for the measurement of weak lensing shear. The NIP channel provides the deep NIR multi-band photometry necessary to derive the photometric redshifts and thus a distance estimate for the lensed galaxies. This paper describes the Imaging Channels design driver requirements to reach the challenging science goals and the design that has been studied during the Cosmic Vision Assessment Phase.