Goldsborough was born at "Hunting Creek", near Cambridge in Dorchester County, Maryland, and pursued an academic course.

He graduated from the University of Pennsylvania at Philadelphia in 1784 and began to study law.

His daughter Maria married Virginia planter and politician William Henry Fitzhugh, son of patriot and planter William Fitzhugh.

In 1790, he was admitted to the bar, and early on held several local political offices.

Goldsborough died at "Shoal Creek" near Cambridge, and is interred there at Christ Episcopal Church Cemetery.