The name has its origin from the Latin cognomen (and later praenomen) Drusus which itself derived from the Greek drosos (dew).
The diminutive "illa" transforms the name into feminine form.
The most notable ancient Roman women bearing the name were members of the Julio-Claudian dynasty, empress Livia Drusilla (wife of emperor Augustus), princesses Julia Drusilla the Elder (sister of emperor Caligula) and Julia Drusilla the Younger (daughter of Caligula).
Women such as the Herodian princess Drusilla and Mauretanian princess Drusilla were named in their honor, thus spreading the name across the Roman Empire.
As a name appearing in the Bible it was adopted by English speakers in the 17th century.