Thielbar's contract was selected by the Twins on Monday, Do-Hyoung Park of MLB.com reports.
The 33-year-old has thrown 98.2 career big-league innings, all with the Twins, though none of those have come since 2015. He owns a lifetime 2.74 ERA and a 1.11 WHIP at the highest level, though the fact that he hasn't been given any major-league opportunities in the last four years indicates that he's unlikely to fill anything other than a low-leverage role.