This paper presents infrared data obtained from observations carried out at the ESO 3.5m New Technology Telescope (NTT) of the Hubble Deep Field South (HDF-S) and the Chandra Deep Field South (CDF-S). These data were taken as part of the ESO Imaging Survey (EIS) program, a public survey conducted by ESO to promote follow-up observations with the VLT. In the HDF-S field the infrared observations cover an area of ~53 square arcmin, encompassing the HST WFPC2 and STIS fields, in the JHKs passbands. The seeing measured in the final stacked images ranges from 0.79 to 1.22 and the median limiting magnitudes (AB system, 2 aperture, 5sigma detection limit) are J_AB~23.0, H_AB~22.8 and K_AB~23.0 mag. Less complete data are also available in JKs for the adjacent HST NICMOS field. For CDF-S, the infrared observations cover a total area of \~100 square arcmin, reaching median limiting magnitudes (as defined above) of J_AB~23.6 and K_AB~22.7 mag. For one CDF-S field H-band data are also available. This paper describes the observations and presents the results of new reductions carried out entirely through the un-supervised, high-throughput EIS Data Reduction System and its associated EIS/MVM C++-based image processing library developed, over the past 5 years, by the EIS project and now publicly available. The paper also presents source catalogs extracted from the final co-added images which are used to evaluate the scientific quality of the survey products, and hence the performance of the software. This is done comparing the results obtained in the present work with those obtained by other authors from independent data and/or reductions carried out with different software packages and techniques. The final science-grade catalogs and co-added images are available at CDS.