Williams, a lineman from Texas, had committed to UConn over the summer, but called the coaches in Storrs on Saturday to tell them he had found a better situation.
That situation is in Oxford, OH where Williams will visit the Miami campus this weekend.
"I have not officially committed," said Williams of Miami. "But I most likely will do so this weekend. They are strong leaders."
Williams attributes his change of heart to a personal evaluation of what he wanted to get out of college.
He cited academics and a promise from Coach Haywood that he could play his preferred position, an assurance he couldn't get from UConn coaches, as the primary reasons for the switch.
Williams was recruited by UConn to play on the offensive line. At Miami he will be a defensive tackle.
"I wanted to play on the defensive side of the ball and the opportunity wasn't there at UConn," said Williams. "They are both good academic schools, but the Farmer School of Business [at Miami] is really good. I read Miami has the number four public business school and top 20 nationally."
Coach Haywood, who was previously the offensive coordinator at Notre Dame, had recruited Williams in his old role.
Williams said the relationship forged during Haywood's initial courtship of him made him comfortable with choosing Haywood as his new head coach.
"Coach Haywood called me the minute he got the job," said Williams. "He reached out to me and told me what he was doing, and how he felt about turning the program around. I was sold on that."
Williams will take this visit to Oxford by himself this weekend, but he may soon be joined by some friends.
He mentioned that a friend of his, whose name he declined to mention because he is still committed to another school, is strongly considering Miami. His best friend, Wes Williams, has also been offered to play for the RedHawks.
Miami's incumbent quarterback, Daniel Raudabaugh, is also a Texas native, leaving Williams little doubt he will have a smooth transition to life up north.
"I've talked to a few players," said Williams. "There are a couple players up there right now from Texas right now, and they love the place. I'm just ready to be a RedHawk."