The trade was announced Thursday at the winter baseball meetings in Dallas.
Casey, who attended Upper St. Clair High School just outside of Pittsburgh, was a fan favorite in Cincinnati, and was highly coveted because of his hitting ability and positive attitude.
"He was a one of a kind, there's no question about that, and I pay him the highest compliments," said Cincinnati General Manager Dan O'Brien. "He really did every thing that the organization ever asked, above and beyond."
Casey, 31, a two-time all-star, has batted better than .300 in five of his last seven seasons and has 1,225 hits in 1,081 career games. He batted .312 with nine home runs and 58 RBI in 2005 while striking out only 48 times in 528 at bats.
Williams has a career 17-26 record.