Ultra-faint dwarf galaxies (UFDs) are promising observable proxies to building blocks of galaxies formed in the early Universe. We study the formation and evolution of UFDs using cosmological hydrodynamic simulations. In particular, we show that a major merger of two building block galaxies with 3,900 Msun and 7,500 Msun at the cosmic age of 510 Myr results in a system with an extended stellar distribution consistent with the de Vaucouleurs profile. The simulated galaxy has an average stellar metallicity of [Fe/H]=-2.7 and features a metallicity gradient. These results closely resemble the properties of a recently discovered UFD, Tucana II, which is extremely metal-poor and has a spatially extended stellar halo with the more distant stars being more metal-poor. Our simulation suggests that the extended stellar halo of Tucana II may have been formed through a past major merger. Future observational searches for spatially extended structures around other UFDs, combined with further theoretical studies, will provide tangible measures of the evolutionary history of the ancient, surviving satellite galaxies.