Wilson was born in Dallas, Texas, the son of Laura Wilson (née Cunningham), a photographer, and Robert Andrew Wilson, an advertising executive and operator of a public television station. His family is Irish and Roman Catholic. Luke has two older brothers, fellow actors Owen and Andrew (the eldest).

Wilson attended St. Mark's School of Texas and Occidental College, where he was initially more interested in the school's athletics department than in drama or theater. He excelled at track and field at Occidental, and later at Texas Christian University, once he transferred.