Williams, who was hired in January 2009 to take over the Bulldogs' football program, allegedly claimed to have been in consideration for a Rhodes Scholarship while a student at Stanford in 1992 but turned down the opportunity to try to catch on with an NFL team.
The New York Times reported that Williams hadn't applied for the Rhodes Scholarship program and Yale then investigated the coach's resume.
In announcing his resignation, which takes effect Dec. 31, Williams said he had been encouraged to apply for a Rhodes Scholarship but didn't.
"I am extremely proud of my academic, athletic and coaching career," Williams said in a statement. "If there was confusion created, I take full responsibility.
"The timing of this inquiry has been difficult for everyone. At this point I believe it is in the best interest of my student-athletes and Yale University that I step down."
The issue arose when Yale quarterback Patrick Witt turned down a Rhodes Scholarship final interview so he could play in the Harvard-Yale game Nov. 19. In interviews at that time Williams mentioned he also refused a Rhodes final interview due to football.
Williams coached at Yale -- his first position as a head coach -- for three seasons, building a 16-14 record. The Bulldogs were 5-5 in 2011, including a 45-7 loss to Harvard.