We present the construction of Dirac sigma models through the generalized gauging procedure of the bosonic 2-dimensional sigma model. Under very mild assumptions, it is shown that this includes only non-minimal coupling to the metric sector, while the gauging of the topological sector can include a richer structure. The gauging here is controlled by two connections on the Dirac structure of the twisted Courant algebroid. Furthermore, we proceed with finding the classical BV action for this gauged action. In this case the AKSZ construction cannot be used so the classical BV action is constructed by directly solving the classical master equation.