The Buffalo Bills released Williams earlier this month, allowing him to sign prior to free agency opening Wednesday at 4 p.m. ET.
Williams, 31, garnered interest on the open market despite having one of his worst seasons in his 10-year pro career in 2015. The pass-rusher was roundly criticized for taking plays off last year and openly questioned his role in Rex Ryan's defense.
Williams is a boom-or-bust player at this stage in his career. Far too often the Dolphins have been on the bust side of their big free agent acquisitions. Tannenbaum is betting that finally changes with Williams.