Dopant atoms can be incorporated into nanowires either via the vapor-liquid-solid mechanism through the catalyst droplet or by the vapor-solid growth on the sidewalls. Si is a typical n-type dopant for GaAs, but in nanowires it often suffers from a strongly amphoteric nature in the vapor-liquid-solid process. This issue can be avoided by using Te, which is a promising but less common alternative for n-type doping of GaAs nanowires. Here, we present a detailed investigation of Te-doped self-catalyzed GaAs nanowires. We use several complementary experimental techniques, such as atom probe tomography, off-axis electron holography, micro-Raman spectroscopy, and single-nanowire transport characterization, to assess the Te concentration, the free-electron concentration, and the built-in potential in Te-doped GaAs nanowires. By combing the experimental results with a theoretical model, we show that Te atoms are mainly incorporated by the vapor-liquid-solid process through the Ga droplet, which leads to both axial and radial dopant gradients due to Te diffusion inside the nanowires and competition between axial elongation and radial growth of nanowires. Furthermore, by comparing the free-electron concentration from Raman spectroscopy and the Te-atom concentrations from atom probe tomography, we show that the activation of Te donor atoms is 100% at a doping level of 4 x 10(18) cm(-3), which is a significant result in terms of future device applications.