The structure of the antiphase domain boundaries of strontium titanate SrTiO3 that exist at temperatures below the antiferrodistortive transition, is analyzed. It is found that some boundaries are similar to Neel domain walls, as an additional component of the order parameter develops within them. We show quantitatively that at low temperatures, typically below similar to 40 K, such boundaries become unstable with respect to the development of a ferroelectric polarization. This ferroelectric transition might provide the much needed explanation for several anomalies that are experimentally observed in SrTiO3 in this temperature region.