Joel was born in 1785 in Harrison, Harrison, West Virginia, United States, the son of unknown parents.
He died in 1830 in McNairy, Tennessee, United States.
His wife was Elizabeth Mary Hood, who he married in 1807 in McNairy, Tennessee, United States. Their ten known children were John Hood (1806-?), Thomas Wallace (1812-1890), Joel Green (1816-?), James K (1821-1897), Stephen Lewis (1822-1887), Jesse (1827-1907), Martha Rebecca (1827-1914), Emily (1828-?), Dorcas (1829-?) and Abijah (1830-?).