This is how I would write it:
Since meeting his lost daughter, his happiness was complete.
Why? Well, since you ask, I'll explain: you are referring to something that has already happened (in the past, thus written in the past tense).
Huh? The words now and is are literally referring to something that is currently happening, not something that has happened, hence why you cannot use them to successfully describe or refer to something that has already happened / occurred in the past.
You could also write (courtesy of Joel Bosveld):
Having met* his lost daughter, his happiness was complete.
UPDATE:
The user "what" is correct - one can indeed use the word "now" in the past tense. I should point out that I was not stating that this could not be done (perhaps what would like to consider the -1!). In such an instance, I would use it like this:
Now that he had finally met his lost daughter, his happiness was restored.
nowthat's the problem (though you should avoid using the word twice in one sentance,) instead it's the wordis. As suchNow that he had met his lost daughter, his happiness was now complete.However a cleaner way to put it might be;His happiness was complete, now that he had met his daughter.– CLockeWork Mar 31 '15 at 08:27nowis indicatingpresent.. Thanks. – Vayth Mar 31 '15 at 09:35nowhelps enhance the sens that the change happened fromthis point. – CLockeWork Mar 31 '15 at 13:09