DFT studies are performed to investigate the structural, mechanical and magneto-electronic properties of the TlTF₃ (T=Fe, Co and Ni) perovskites for the first time using GGA, GGA+U and hybrid density functional theory (HF). Our calculations show that HF give better results than GGA and GGA+U and more consistent with the experiments. The comparison of the lattice constants calculated by HF with experiments shows a maximum underestimation less than 0.2%. The chemical bonding between different ions in these compounds is explained on the bases of electronic clouds, which reveals that in TlFeF₃, Fe has more ionic character with F than the rest. The mechanical properties explain the hardness of these compounds and show that TlFeF₃ is more ductile. Spin-dependent electronic band profiles show that TlFeF₃ and TlCoF₃ are metallic, whereas TlNiF₃ is pseudo direct wide bandgap semiconductor. The stable magnetic phase optimizations and the calculated magnetic susceptibility confirm that TlFeF₃ and TlNiF₃ are ferromagnetic whereas TlCoF₃ is anti-ferromagnetic material.