Walker was born near Russelville in Logan County, Kentucky. He attended private schools in Kentucky and Tennessee and studied law. He moved to Florida in 1837, settling in Leon County. He was elected to the first session of the Florida State Legislature in 1845, serving Wakulla and Leon Counties as Senator. In 1848, he was elected by Leon County to the Florida House of Representatives.
He served from 1849 to 1854 as the Register of Public Lands and was ex oficio State Superintendent of Public Instruction. He advocated and promoted interest in public schools. His efforts resulted in the creation of public schools in Tallahassee. He served as Mayor of Tallahassee. In 1860, he became a Florida Supreme Court Justice, but resigned to run to become Governor.
He had been a Whig and was a Constitutional Unionist and so had opposed Florida's secession. However, when the decision was passed to leave the Union, he supported his state. After the war, he was appointed governor on December 20, 1865 by President Andrew Johnson. His term in office was devoted to restoring the state government while Florida was under military occupation during Reconstruction. After leaving the governor's office on July 4, 1868, he returned to practicing law. In 1878, he was appointed circuit court judge, a position he held until his death on July 20, 1891.