Aristarchus Champion was born in Westchester, Connecticut on October 23, 1784 to General Henry Champion and Abigail Tinker. His twin brother was named Aristobulus. His paternal grandparents were Colonel Henry and Deborah (Brainard) Champion of Westchester, and his maternal grandparents were Sylvanus and Abigail (Olmstead) Tinker of East Haddam. Both General and Colonel Henry Champion participated in the Revolutionary War.

Aristarchus graduated from Yale College in 1807 and studied law, but later took over management of his father's estates in both Ohio and Western New York. He settled in Rochester, New York in 1826 and invested further in real estate. The wealthiest citizen of the young village and, later, city, Aristarchus was a benefactor of religious and philanthropic effects. He served as Vice President of the American Bible Society from 1844 until his death and as President of the American Home Missionary Society from 1858 to 1860. He was also a benefactor of Yale College, specifically in the creation of the professorship of the Pastoral Charge in the Divinity School in 1839.

Aristarchus never married and left most of his property to religious and charitable societies, particularly the American Bible Society and the Presbyterian Board of Foreign Missions, when he died on September 18, 1871.