Butler was signed by the Dolphins on Thursday, Omar Kelly of the Sun-Sentinel reports.
Butler, who was cut by the Cardinals a little over a week ago, adds a veteran presence to a thin linebackers group. The 27-year-old could be ready in time for Sunday's tilt with the Patriots, but more information will be known as the week progresses. Butler figures to serve in a backup role, as he'll compete with Spencer Paysinger, Neville Hewitt, and Mike Hull for reps.