<p>In this article, we propose three gravastar models within the framework of <i>f</i>(<i>T</i>) gravity, inspired by the Mazur-Mottola conjecture as a viable alternative to black holes. Each gravastar consists of three distinct regions: (i) the interior core region, (ii) the intermediate thin shell, and (iii) the exterior spherical region. The exterior region can be characterized by the Schwarzschild-de Sitter solution and other novel solutions. With these specifications, we have derived a set of exact, singularity-free solutions for the gravastar, showcasing several physically interesting and valid features within the context of alternative gravity. The field equations for the shell case were solved using a novel technique based on Killing vectors, avoiding the approximations commonly employed in previous studies. Additionally, we analyzed several physical properties of the thin shell, including its proper length, entropy, energy content, and the relevant energy conditions.</p>