Grayson was born to Dr. John Cooke Grayson (a descendant of American George Mason, one of the American Founding Fathers) and Frances Adelena Pettus at Salubria, the Grayson family estate in Culpeper County, Virginia. He graduated Phi Beta Kappa with a bachelor's degree from the College of William and Mary in 1898. He studied for three years at the Medical College of Virginia before leaving to attend the University of the South. After a year there, he received his M.D. as well as his Doctor of Pharmacy. He interned for a year at Columbia Hospital for Women in Washington, D.C.