Abstract The regularization properties of the total generalized variation (TGV) functional for the solution of linear inverse problems by means of Tikhonov regularization are studied. Considering the associated minimization problem for general symmetric tensor fields, the well-posedness is established in the space of symmetric tensor fields of bounded deformation, a generalization of the space of functions of bounded variation. Convergence for vanishing noise level is shown in a multiple regularization parameter framework in terms of the naturally arising notion of TGV-strict convergence. Finally, some basic properties, in particular non-equivalence for different parameters, are discussed for this notion.