Breaking the time reversal symmetry of a topological insulator, for example by the presence of magnetic ions, is a prerequisite for spin-based electronic applications in the future. In this regard Mn-doped Bi₂Te₃ is a prototypical example that merits a systematic investigation of its magnetic properties. Unfortunately, Mn doping is challenging in many host materials - resulting in structural or chemical inhomogeneities affecting the magnetic properties. Here, we present a systematic study of the structural, magnetic and magnetotransport properties of Mn-doped Bi₂Te₃ single crystals using complimentary experimental techniques. These materials exhibit a ferromagnetic phase that is very sensitive to the structural details, with T_C varying between 9 and 13 K (bulk values) and a saturation moment that reaches 4.4(5) μ_B per Mn in the ordered phase. Muon spin rotation suggests that the magnetism is homogeneous throughout the sample. Furthermore, torque measurements in fields up to 33 T reveal an easy axis magnetic anisotropy perpendicular to the ab-plane. The electrical transport data show an anomaly around T_C that is easily suppressed by an applied magnetic field, and also anisotropic behavior due to the spin-dependent scattering in relation to the alignment of the Mn magnetic moment. Hall measurements on different crystals established that these systems are n-doped with carrier concentrations of ∼0.5-3.0 × 10²⁰ cm^-3. X-ray magnetic circular dichroism (XMCD) at the Mn L_2,3 edge at 1.8 K reveals a large spin magnetic moment of 4.3(3) μ_B/Mn, and a small orbital magnetic moment of 0.18(2) μ_B/Mn. The results also indicate a ground state of mixed d⁴-d⁵-d⁶ character of a localized electronic nature, similar to the diluted ferromagnetic semiconductor Ga_1-xMn_xAs. XMCD measurements in a field of 6 T give a transition point at T ≈ 16 K, which is ascribed to short range magnetic order induced by the magnetic field. In the ferromagnetic state the easy direction of magnetization is along the c-axis, in agreement with bulk magnetization measurements. This could lead to gap opening at the Dirac point, providing a means to control the surface electric transport, which is of great importance for applications.