Clinton signed it because the Republicans had enough votes to override his veto. By signing it he was able to take credit for it.
It was one of the top 4 or 5 bills passed in a 50 year period.
Clinton was able to round up enough Democrats to vote for it to give him cover and that's why it looks like there were enough votes for an override. If clinton had opposed it, then most of the Demos would have done so as well.
Don't forget that he vetoed the same bill twice earlier but had a couple of small provisions made (cosmetic changes) and then he signed it. There were no overrides of the first 2 vetoes.