I'm interested in pursuing a PhD program but will not complete my undergraduate degree until December. Most PhD programs require their application to be completed in December. Does that mean I have to wait an extra year to apply (since it could take a few weeks past their deadline to receive my final transcripts)?
Certainly not. Most students graduate in the spring, but apply to graduate school several months before graduation. It is not expected that you will have your final transcript in hand when you apply. However, it is expected that you will have the transcript prior to the actual start of your graduate school studies.
Most PhD admission have a 'provisional acceptance' scheme that would enable you to apply for the degree even if you're in the final semester of the qualifying degree.
Does that mean I have to wait an extra year to apply?
No. Most institutions (at least in Asia) allow PhD applications for every semester. So a year-long wait won't be necessary.