Born in New Boston, New Hampshire, Cochrane moved to Montgomery County, New York.

He was admitted to the bar in 1841 and practiced in Amsterdam 1841–1851, Schenectady 1851–1855, and Albany, New York, from 1855 until his death.

Cochrane was elected as a Republican a member of the New York State Assembly (Montgomery Co.) in 1844.

He was interred in Green Hill Cemetery, Amsterdam, New York.

This article incorporates public domain material from the Biographical Directory of the United States Congress