The first publicly known key-agreement protocol that meets these criteria was Diffie-Hellman key exchange, in which the two people jointly exponentiate a generator with random numbers, in such a way that an eavesdropper has no way of guessing what the key is.
Diffie-Hellman was first developed by researchers at GCHQ, the UK equivalent to NSA. James Ellis demonstrated that non-secret encryption was possible in the 1960s and Malcolm Williamson developed what is now called Diffie-Hellman Key exchange in the early 1970s. GCHQ did not allow publication, so Diffie and Hellman were the first to publish.
See also : ISAKMP
See the appendix to Crypto, by Steven Levy for more information on GCHQ's work, The Code Book by Simon Singh, or the GCHQ Web page about 'non-secret encryption'. The latter contains an essay by James Ellis himself.Reference