Whitfield Diffie and Martin Hellman were the first to show, in a paper published in 1976, that a code could be devised that was encoded using one key and decoded using another.
James Ellis wrote a paper in 1970 on similar work done by himself and Clifford Cocks, but it was covered by the UK's Official Secrets Act, and was not published until many years later.
Using the Diffie-Hellman (D-H) algorithm, one key is specifically for encryption and the other for decryption - you can't use them the other way around. This makes it unsuitable for a PKI system as normally used.