Castle was the last Republican elected governor of the state, serving from 1985 to 1992. He then went on to serve nine terms in Congress.
"As governor and our state's longest-serving U.S. representative, he embodied what it means to lead with principle, decency, and dedication," said Governor Matt Meyer in a statement. "Governor Castle was a leader in a generation of Delawareans who put people before politics - whose bipartisan spirit and dedication to service set a standard to which we all aspire."
Castle retired from politics after losing the Delaware Republican primary for U.S. Senate in 2010.