Glennon was born in The Woodlands, Texas to John and Nancy Glennon. John, his father, had a position with Exxon Mobil that forced the family to move three times in Sean's grade-school years. From The Woodlands, the family would move to New Jersey, back to Texas, then finally to Centreville, Virginia, where they would stay for Glennon's high school years. His sister Katie also attended Virginia Tech. His brother Mike played for North Carolina State University, and was drafted by the Tampa Bay Buccaneers in the 2013 NFL Draft.