Moderna and Pfizer submitted for approval shortly after they released their initial Phase 3 results. Approval is expected to be expedited, but will not be instant (I've read a few weeks, assuming no problems). Oxford/AstraZeneca will likely follow the same course now that their results are available (they were waiting for enough people in their trials to become infected, same as the other Phase 3 trials).

It is widely expected that large scale distribution of these vaccines will begin in late December.