Ni4Ti3 precipitates, which generally exist in aged Ni-rich NiTi shape memory alloys (SMAs), can have a profound effect on material properties. However, the fundamental insights into the effects of Ni4Ti3 precipitates on the functional properties, including the superelasticity (SE), elastocaloric effect (eCE), and shape memory effects (SMEs), are not well understood yet, especially those originating from the B2-B19′ martensite transformation (MT). In this work, a phase field model coupling the precipitation of Ni4Ti3 and the B2-B19′ MT is proposed, where the thermo-mechanical coupling effect and grain size effect are considered. The precipitate-dependent SE, eCE, one-way SME (OWSME), and stress-assisted two-way SME (SATWSME) of single-crystal, polycrystalline, and gradient-nanograined NiTi SMAs are simulated. The effects of the precipitate density, grain orientation range (texture), and gradient-distributed precipitate are examined, and the underlying microscopic mechanisms are revealed. The simulation results and new findings not only contribute to a more comprehensive insight into the effect of Ni4Ti3 precipitates on the MT, martensite reorientation, and functional properties of NiTi SMAs but also provide a reference for the development of excellent SMA-based solid refrigerants or SMA smart materials with designable functional properties.