The 38-year-old Williams was a defensive assistant for the NFL's Jacksonville Jaguars the past two years.
He is the 33rd head coach of the Yale Bulldogs.
"I am thrilled for this tremendous opportunity to be the head football coach at such a historic and fabled institution," Williams said.
Williams succeeds Jack Siedlecki, who retired after 12 seasons and became an assistant athletic director.
Yale was 6-4 this season.