Melton, nicknamed Beltin' Bill, made his major-league debut with the White Sox in May 1968 at 22 years old.
"Bill was a friend to many at the White Sox and around baseball, and his booming voice will be missed. Our sympathies go out to his wife Tess, and all of their family and friends," White Sox Chairman Jerry Reinsdorf said.
During his eight-year run with Chicago, Melton ranked 11th among the AL leaders in homers and RBI. His 154 home runs currently rank ninth on the club's all-time list.
Melton returned to Chicago in 1992 as a team ambassador and part-time scout.
He worked with basketball Hall of Famer Michael Jordan following Jordan's first retirement from the National Basketball Association in 1993, serving as one of his hitting instructors.
In 1998, Melton joined the White Sox television broadcast team as an analyst for the pre-game and postgame shows. He retired in 2020.
Melton died in Phoenix after a brief illness. He was 79 years old.
He is survived by his wife Tess, son Billy, daughter Jennifer, a grandson and many extended family members.