Context. Central starbursts in galaxies are an extreme example of ongoing galaxy evolution. The outer parts of galaxies contain a fossil record of galaxy formation and evolution processes in the more distant past. The characterization of resolved stellar populations allows one a detailed study of these topics. Aims: We observed the outer parts of NGC 1569 and NGC 4449, two of the closest and strongest dwarf starburst galaxies in the local universe, to characterize their stellar density and populations, and obtain new insights into the structure, formation, and evolution of starburst galaxies and galaxy halos. Methods: We obtained HST/WFPC2 images between 5 and 8 scale radii from the center, along the intermediate and minor axes. We performed point-source photometry to determine color magnitude diagrams of I vs. V - I. We compared the results at different radii, including also our prior HST/ACS results for more centrally located fields. Results: We detect stars in the RGB and TP-AGB (carbon star) phases in all outer fields, but not younger stars such as those present at smaller radii. The RGB star density profile is well fit by either a de Vaucouleurs profile or a power-law profile, but has more stars at large radii than a single exponential. To within the uncertainties, there are no radial gradients in the RGB color or carbon-to-RGB-star ratio at large radii. Conclusions: The galaxies have faint outer stellar envelopes that are not tidally truncated within the range of radii addressed by our study. The density profiles suggest that these are not outward extensions of the inner disks, but are instead distinct stellar halos. This agrees with other work on galaxies of similar morphology. The presence of such halos is consistent with predictions of hierarchical galaxy formation scenarios. The halos consist of intermediate-age/old stars, confirming the results of other studies that have shown the starburst phenomenon to be very centrally concentrated. There is no evidence for stellar-population age/metallicity gradients within the halos themselves.