Born in Petersham, Massachusetts, Bigelow was graduated from Williams College, Williamstown, Massachusetts, in 1803. He studied law. He was admitted to the bar and commenced practice in Petersham. He served as member of the State senate 1819–1821. He was editor of the first seventeen volumes of Massachusetts Reports and of a digest of six volumes of Pickering's Reports.
Bigelow was elected as a Federalist to the Seventeenth Congress (March 4, 1821 – March 3, 1823). He moved to Peoria, Illinois, in 1831 and continued the practice of law. He was interested in the real estate business and in the operation of ferry boats. He served as Justice of the Peace. He was appointed clerk of the circuit court of Peoria County, November 26, 1835, and served until his death in Peoria, Illinois, October 2, 1838. He was interred presumed to be in the Old Centre Cemetery, Petersham, Massachusetts.
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