Paleomagnetic studies of meteorites constrain the evolution of magnetic fields in the early solar system. These studies rely on the identification of magnetic minerals that can retain stable magnetizations over ≳4.5 billion years (Ga). The ferromagnetic mineral tetrataenite (γ’-Fe_0.5Ni_0.5) is found in iron, stony-iron and chondrite meteorite groups. Nanoscale intergrowths of magnetostatically-interacting tetrataenite have been shown to carry records of paleomagnetic fields. Tetrataenite can also occur as isolated, non-interacting grains in many meteorite groups. Here we study non-interacting tetrataenite to establish the grain size range over which it can retain magnetization that is stable over solar system history. We present the results of analytical calculations and micromagnetic modelling of isolated tetrataenite grains with various sizes and geometries. We find that tetrataenite forms a stable single domain state for grain lengths between ~10 and 160 nm dependent on its axial ratio. It also possesses a magnetization resistant to viscous remagnetization over the lifetime of the solar system at 293 K. At smaller grain sizes, tetrataenite is superparamagnetic while at larger grain sizes, tetrataenite’s lowest energy state is a lamellar two-domain state that is stable over Ga-scale timescales. Unlike many other ferromagnetic minerals, tetrataenite does not form a single-vortex domain state due to its large uniaxial anisotropy. Our results show that both single domain and two-domain tetrataenite carry extremely stable magnetization and therefore are promising for paleomagnetic studies.