Electrocardiographic imaging (ECGI) is a clinical and research tool for noninvasive diagnosis of cardiac electrical dysfunction. The position of the heart within the torso is both an input and common source of error in ECGI. Many studies have sought to improve cardiac localization accuracy, however, few have examined quantitatively the effects of uncertainty in the position of the heart within the torso. Recently developed uncertainty quantification (UQ) tools enable the robust application of UQ to ECGI reconstructions. In this study, we developed an ECGI formulation, which for the first time, directly incorporated uncertainty in the heart position. The result is an ECGI solution that is robust to variation in heart position. Using data from two Langendorff experimental preparations, each with 120 heartbeats distributed across three activation sequences, we found that as heart position uncertainty increased above ±10 mm, the solution quality of the ECGI degraded. However, even at large heart position uncertainty (±40 mm) our novel UQ-ECGI formulation produced reasonable solutions (root mean squared error < 1 mV, spatial correlation >0.6, temporal correlation >0.75).