Ten Eyck was born on April 18, 1779, in Schodack, New York. He was the son of Anthony E. Ten Eyck (1739–1816) and Maria (née Egbert) Ten Eyck (1748–1819). His father was a member of Constitutional Convention of 1787, judge of Rensselaer County and member of the New York State Senate. He had several siblings including Anthony Ten Eyck (1784–1859), Jacob A. Ten Eyck (1781–1859), Coenraad Anthony Ten Eyck (1789–1845), Sheriff of Albany County.