Stockbridge was born in Bath, Maine and attended the common schools. He clerked at a wholesale house in Boston 1843-1847. He moved to Chicago and opened a lumber yard. He then moved to Saugatuck, Michigan in 1851 and engaged in the operation of sawmills. He was also interested in mercantile pursuits. He moved to Kalamazoo in 1863 and engaged in the lumber business there. He was a member of the Michigan State House of Representatives in 1869 and a member of the Michigan State Senate in 1871. Stockbridge was appointed ambassador to the Netherlands on July 12, 1875. He took the oath of office but never proceeded to the post. He was elected as a Republican to the United States Senate in 1887 and was reelected in 1893. He served from March 4, 1887 until his death on April 30, 1894. He was chairman of the Committee on Fisheries in the Fiftieth through Fifty-second Congresses. He died suddenly while visiting his nephew James Houghteling in Chicago. He is interred in Mountain Home Cemetery in Kalamazoo, Michigan.

In 1882, Stockbridge purchased the site of the famous Grand Hotel on Mackinac Island and arranged financing for its construction from the three major transportation companies that rendered service to the island at the time: the Michigan Central Railroad, the Grand Rapids and Indiana Railroad, and the Detroit and Cleveland Navigation Company. Together, they formed the Mackinac Island Hotel Company, which then built the Grand Hotel in 1887.

Stockbridge was the last person to have served in the Michigan State Legislature and in the United States Senate until Debbie Stabenow was elected in 2000.