Ozra Hadley was born in Cherry Creek, New York and was educated in the public schools of New York. He attended Fredonia Academy (now SUNY-Fredonia).
Hadley moved to Minnesota in 1855 becoming a farmer, before entering politics being appointed county auditor. In 1865, after the American Civil War, he moved to Arkansas where he went into business as a storeowner.
Hadley served in the Arkansas Senate from 1869 to 1871 and was president of the Senate in 1871. In 1871, as part of a political compromise (see: Brooks-Baxter War) he became Governor of Arkansas after Governor Powell Clayton resigned.
During his term he sided with the 'Radical Republicans' and denied assistance to reenfanchised whites. Hadley left office in 1873.
After his term Hadley served as registrar of the U.S. Land Office and received an appointment as postmaster of Little Rock, Arkansas where he served from 1878 to 1882.
Ozra Hadley died in Watrous, New Mexico (which is now a ghost town) in Mora County, New Mexico, where he owned a ranch.