The theoretical aspects of evaluating the electrical resistance of a thermoelectric leg–metal contact are considered. A physical model of such a contact and methods for calculating the main components of the contact resistivity, namely, the resistivity of the interfacial layer and the resistivity related to the transfer of charge carriers through a potential barrier at the boundary between a material of the thermoelectric leg and a metal, are proposed. The contact resistivity for thermoelectric legs made of Bi2Te3 based materials with deposited antidiffusion nickel layers is calculated. It was established that the contact resistivity in such thermoelements reaches a value from 0.25 × 10−6 to 2.5 × 10−6 Ω cm2 and depends on the temperature and interfacial layer thickness. It is demonstrated that the findings are in good agreement with the known experimental values of contact resistivity.