Mastro Auction in Burr Ridge, Ill., handed the ball over to lawyers for Williams' daughter Thursday after verifying the signature, the Chicago Sun-Times reported.
"My dad asked one person for an autograph in his life -- it was Babe Ruth, and it was on this ball,'' said Claudia Williams. "I grew up my whole life hearing how my dad met Babe Ruth and got this ball.''
Williams was in his 20s when he met Ruth and got the autograph. He was so pleased with the inscription -- "To my pal Ted Williams"-- that he told interviewers he often used the same phrase when he gave autographs.
The two greats both played for the Boston Red Sox, Williams for most of his career and Ruth briefly before being traded to the New York Yankees.
Williams, who died several years ago, offered a $5,000 reward to no avail when the ball was stolen.
Claudia Williams plans to give the ball to the Ted Williams Museum & Hitters Hall of Fame in St. Petersburg, Fla.