BYU web page indicating that the First Presidency oversees the Board of Trustees.
Brigham Young University. Administration
Church Board of Education and Board of Trustees
President Russell M. Nelson Chairman
President Dallin H. Oaks First Vice Chairman
President Henry B. Eyring Second Vice Chairman
Elder Jeffrey R. Holland Board Member
Elder David A. Bednar Board Member
Elder Quentin L. Cook Board Member
Elder Dale G. Renlund Board Member
Elder Robert C. Gay Board Member
Elder Michael T. Ringwood Board Member
Bishop Gérald Caussé Board Member