Regularizing the least-squares criterion with the total number of coefficient changes, it is possible to estimate time-varying (TV) autoregressive (AR) models with piecewise-constant coefficients. Such models emerge in various applications including speech segmentation, biomedical signal processing, and geophysics. To cope with the inherent lack of continuity and the high computational burden when dealing with high-dimensional data sets, this paper introduces a convex regularization approach enabling efficient and continuous estimation of TV-AR models. To this end, the problem is cast as a sparse regression one with grouped variables, and is solved by resorting to the group least-absolute shrinkage and selection operator (Lasso). The fresh look advocated here permeates benefits from advances in variable selection and compressive sampling to signal segmentation. An efficient block-coordinate descent algorithm is developed to implement the novel segmentation method. Issues regarding regularization and uniqueness of the solution are also discussed. Finally, an alternative segmentation technique is introduced to improve the detection of change instants. Numerical tests using synthetic and real data corroborate the merits of the developed segmentation techniques in identifying piecewise-constant TV-AR models.