Van Rensselaer was born in New York City, the eldest child of Stephen Van Rensselaer II, the ninth patroon of Rensselaerswyck, a large land grant in upstate New York awarded by the Dutch to his ancestor Kiliaen Van Rensselaer.
Van Rensselaer began attending Princeton College; since it was near to battles of the ongoing American Revolution, he was later sent to Harvard College, from which he graduated Phi Beta Kappa[REF] in 1782 [REF].