Joseph Estabrook was born in Lebanon, New Hampshire to Hobart and Ann (Hyde) Estabrook on December 7, 1792. He graduated from Dartmouth College in 1815 and entered Princeton to pursue a career in the ministry, but a throat affliction forced him to abandon this calling. He became a teacher instead and began working as the principal of Amherst Academy in 1817. When the school was reorganized as Amherst College in 1821, Estabrook became a professor of Greek and Latin. Throughout his time at Amherst, he was known as something of an eccentric, using snuff prodigiously and shocking the townsfolk by firing a gun on Sunday. Estabrook married Nancy Dickinson (1806-1846) in 1823 and the couple moved to Staunton, Virginia in 1824. Here, Estabrook served as the principal of a school for girls. He came to Knoxville in 1834 as the President of the Knoxville Female Academy and became the President of East Tennessee University in 1840.

During his administration, Estabrook relaxed discipline, created a faculty of scholarly professors, and oversaw the building program that led to the construction of the East and West College buildings. Courses of instruction became more organized, catalogs were published for the first time, an alumni association was formed, and the first literary societies, Philomathesian and Chi Delta, were created. The school also assumed its military character during this time. Estabrook resigned in 1850 to found the Salt Works at Oliver Springs, Tennessee. He married Angelina Matilda Wiley (born 1834) on April 9, 1853 and the couple had one son, Joseph Jr., who died in a fall at the age of 13 months. Joseph Estabrook died on May 18, 1855 in Knoxville and was buried next to his son. Both were moved to the Oliver Springs Cemetery in 1888.