Jeremiah Van Rensselaer was born on August 27, 1738 at the main home of his family's manor, "Rensselaerswyck" in what is now Watervliet, New York.
His parents were Johannes Van Rensselaer (1708–1793) and Engeltie "Angelica" Livingston (1698–1747), who married in 1734.
He was the third of six children: Catherine (b. 1734), Margarita (b. 1736), Jeremiah, Robert (b. 1740), Hendrick (b. 1742), and James (b. 1747).
 His mother died before he was 10 years-old and his father remarried, to Gertrude van Cortlandt.

His older sister was Catherine van Rensselaer (1734–1803) who in 1755 married Philip Schuyler (1733–1804), a Revolutionary general and United States Senator from New York.
This relationship made him the maternal uncle to Angelica Schuyler (1756-1814), who married British MP John Barker Church, Elizabeth Schuyler (1757-1854), who married Alexander Hamilton, the first United States Secretary of the Treasury, Margarita Schuyler (1758-1801), who married Stephen Van Rensselaer III, the son of Jeremiah's first cousin, Stephen van Rensselaer II (1742–1769), and Philip Jeremiah Schuyler (1768-1835), who also served in the United States House of Representatives.

His younger brother was Robert Van Rensselaer (1740–1802), a Brigadier General during the Revolutionary War, a member of the New York Provincial Congress from 1775 to 1777 and later a member of the New York State Assembly in the 1st, 2nd and 4th New York State Legislatures.
Robert's son and Jeremiah's nephew was Jacob Van Rensselaer (1767–1835), a Federalist member of the New York State Assembly and the Secretary of State of New York from 1813 to 1815.
Jeremiah Van Rensselaer was born on August 27, 1738 at the main home of his family's manor, "Rensselaerswyck" in what is now Watervliet, New York. His parents were Johannes Van Rensselaer (1708–1793) and Engeltie "Angelica" Livingston (1698–1747), who married in 1734. He was the third of six children: Catherine (b. 1734), Margarita (b. 1736), Jeremiah, Robert (b. 1740), Hendrick (b. 1742), and James (b. 1747).  His mother died before he was 10 years-old and his father remarried, to Gertrude van Cortlandt.
His older sister was Catherine van Rensselaer (1734–1803) who in 1755 married Philip Schuyler (1733–1804), a Revolutionary general and United States Senator from New York. This relationship made him the maternal uncle to Angelica Schuyler (1756-1814), who married British MP John Barker Church, Elizabeth Schuyler (1757-1854), who married Alexander Hamilton, the first United States Secretary of the Treasury, Margarita Schuyler (1758-1801), who married Stephen Van Rensselaer III, the son of Jeremiah's first cousin, Stephen van Rensselaer II (1742–1769), and Philip Jeremiah Schuyler (1768-1835), who also served in the United States House of Representatives.
His younger brother was Robert Van Rensselaer (1740–1802), a Brigadier General during the Revolutionary War, a member of the New York Provincial Congress from 1775 to 1777 and later a member of the New York State Assembly in the 1st, 2nd and 4th New York State Legislatures. Robert's son and Jeremiah's nephew was Jacob Van Rensselaer (1767–1835), a Federalist member of the New York State Assembly and the Secretary of State of New York from 1813 to 1815.
Jeremiah Van Rensselaer