ARPA - DoD directive 5105.15 establishing the Advanced Research Projects Agency (ARPA) was signed on February 7, 1958. The directive gave ARPA the responsibility "for the direction or performance of such advanced projects in the field of research and development as the Secretary of Defense shall, from time to time, designate by individual project or by category."
DARPA - On March 23, 1972, by DoD Directive, the name was changed to the Defense Advanced Research Projects Agency (DARPA). DARPA was established as a separate defense agency under the Office of the Secretary of Defense.
ARPA - On February 22, 1993, DARPA was redesignated the Advanced Research Projects Agency (ARPA) -- as the agency was known before 1972. The change was outlined in President Bill Clinton's strategy paper, "Technology for America's Economic Growth, A New Direction to Build Economic Strength."
DARPA - On February 10, 1996, Public Law 104-106, under Title IX of the Fiscal Year 1996 Defense Authorization Act, directed an organizational name change to the Defense Advanced Research Projects Agency (DARPA).