Daniel Grosvenor was born in Pomfret, Connecticut, on April 20, 1750, the son of Ebenezer Grosvenor (1713-1793) and Lucy Cheney (1720-1792). He had nine siblings: Ebenezer (1739-1788), Elizabeth (b. 1740), Oliver (b. 1743), Asa (1766-1834), Lucy (b. 1747), Lemuel (b. 1752), Ezra (b. 1755), Chloe (b. 1757), and Nathan (b. 1764).
After graduating from Yale College in 1769, Daniel Grosvenor served as pastor of the Congregational Church at Grafton, Connecticut (1774-1787), and Paxton, Massachusetts (1794-1802). He left each on account of health problems. Grosvenor lived in Petersham, Massachusetts, until his death on July 22, 1834. He married Deborah Hall (1756-1841) on May 9, 1776, and they had ten children: Daniel Bulkeley (1777-1822), Jonathan Prescott (1779-1854), David Hall (1779-1842), Deborah Hall (b. 1781), Ebenezer Oliver (b. 1783), Lucy Williston (1785-1861), Ira Rufus (b. 1787), Elizabeth Sophia (b. 1789), Cyrus Pitt (1792-1879), and Moses Gill (1796-1879). Moses Gill Grosvenor graduated from Dartmouth College in 1822, studied at the Andover Theological Seminary between 1823 and 1825, and later lived in Haverhill, Massachusetts, and Acworth, New Hampshire.