Integrated communications and localization (ICAL) will play an important part in future sixth generation (6G) networks for the realization of Internet of Everything (IoE) to support both global communications and seamless localization. Massive multiple-input multiple-output (MIMO) low earth orbit (LEO) satellite systems have great potential in providing wide coverage with enhanced gains, and thus are strong candidates for realizing ubiquitous ICAL. In this paper, we develop a wideband massive MIMO LEO satellite system to simultaneously support wireless communications and localization operations in the downlink. In particular, we first characterize the signal propagation properties and derive a localization performance bound. Based on these analyses, we focus on the hybrid analog/digital precoding design to achieve high communication capability and localization precision. Numerical results demonstrate that the proposed ICAL scheme supports both the wireless communication and localization operations for typical system setups.