What happened in 1999 was simply the replacement of the term Ecu (european currency unit) in the "books" for Euro. The ecu wasnt real currency and neither was the euro in 1999. It didnt truly exist until 2002.
It has been a long process which you could say started in 1975 (when the "European unit of account" was created, which got replaced by the term European currency unit in 1979). But for the general public 2002 was the year it got introduced.
I guess you could say in short: if it is the concept, it is 1975 same thing as in 1999 just a different name. If it is the name, it would be 1995. If it is the actual legal currency people can pay with it is 2002.