Henry Clay Baker was the son of Dorsey Syng Baker (1823-1888) and Caroline Tibbetts (died circa 1863), and the grandson of Gideon Tibbetts (1808-1887) and Mary Fox Tibbetts (1815-1901). Dorsey Syng Baker crossed the plains to Oregon in 1848. After living briefly in California, Baker returned to Oregon in the early 1850s. In 1850, he married Caroline Tibbetts and they had four children. Baker was educated as a physician but eventually ventured into a variety of businesses, such as a store, steamboats, and railway lines. He built the second rail line in the Pacific Northwest, which was named the "Rawhide Railroad." He also established, with John F. Boyer, one of the first banks in eastern Washington.

The Tibbetts family was connected to the Bakers through the marriage of Caroline Tibbetts to Dorsey Syng Baker. Gideon and Mary Tibbetts arrived in Oregon in 1847. A few years later, Gideon Tibbetts moved his family to East Portland and took over a homestead originally held by a family named Dobbins. This area, about 600 acres, was known as Tibbetts Addition. Gideon also served one term in the Oregon Legislature.