We describe the creation of a set of artificially "redshifted" galaxies in the range 0.1 < z < 1.1 using a set of ~100 SDSS low-redshift (v < 7000 km s-1) images as input. The intention is to generate a training set of realistic images of galaxies of diverse morphologies and a large range of redshifts for the GEMS and COSMOS galaxy evolution projects. This training set allows other studies to investigate and quantify the effects of cosmological redshift on the determination of galaxy morphologies, distortions, and other galaxy properties that are potentially sensitive to resolution, surface brightness, and bandpass issues. We use galaxy images from the SDSS in the u, g, r, i, and z filter bands as input, and computed new galaxy images from these data, resembling the same galaxies located at redshifts 0.1 < z < 1.1 and viewed with the Hubble Space Telescope Advanced Camera for Surveys (HST ACS). For this process we take into account angular size change, cosmological surface brightness dimming, and spectral change. The latter is achieved by interpolating a spectral energy distribution that is fit to the input images on a pixel-to-pixel basis. The output images are created for the specific HST ACS point-spread function and the filters used for GEMS (F606W and F850LP) and COSMOS (F814W). All images are binned onto the desired pixel grids (0.03'' for GEMS and 0.05'' for COSMOS) and corrected to an appropriate point-spread function. Noise is added corresponding to the data quality of the two projects, and the images are added onto empty sky pieces of real data images. We make these data sets available on our Web site, as well as the code—FERENGI (Full and Efficient Redshifting of Ensembles of Nearby Galaxy Images)—to enable data sets for other redshifts and/or instruments to be produced.