Webb was born Webb Parmelee Hollenbeck in Indianapolis, Indiana. He was the only child of Jacob Grant Hollenbeck (1867 – May 2, 1939), the ticket-clerk son of a grocer from an Indiana farming family, and his wife, the former Mabel A. Parmelee (Parmalee or Parmallee; March 24, 1869 – October 17, 1960), the daughter of David Parmelee, a railroad conductor. The couple married in Kankakee, Illinois, on January 18, 1888, and separated in 1891, shortly after their son's birth. According to Marion County, Indiana, marriage records, they married in Indianapolis on January 18, 1888.
In 1892, Webb's mother, now called "Mabelle", moved to New York City with her beloved "little Webb", as she called him for the remainder of her life. She dismissed questions about her husband, Jacob, who like her father, worked for the Indianapolis-St. Louis Railroad, by saying, "We never speak of him. He didn't care for the theatre." The couple apparently divorced, since by 1900, Mabelle was married to Green B. Raum, Jr. New York City's 1900 U.S. census indicates Mabelle and her son were using the surname Raum and living on West 77th Street with Green Berry Raum, Jr., a copper-foundry worker, who gave his position in the household as Mabel's husband. Raum was the son of General Green Berry Raum, former U.S. Commissioner of Internal Revenue and former U.S. Commissioner of Pensions. Webb's father, Jacob, married, as his second wife, Ethel Brown, and died in 1939.