Joshua Maddox was born and educated in England. When he emigrated to America he lived briefly in New Jersey before settling in Philadelphia, where he became a successful merchant. Maddox married Mary Rudderow, the widow of wealthy Frenchman Nicholas Gaulan. He was also a warden of Christ Church.
Maddox was politically active in Philadelphia. He was a member of the city’s Common Council from 1739-1741, and then, from 1741 until his death in 1759, he served as a judge of various county courts.
Maddox was a founder and trustee of the College and Academy of Philadelphia (now the University of Pennsylvania) until his death in 1759.