You will not be able to apply to take the exam until your school verifies that you have completed all of the required coursework. For my school, I was able to have my official transcript sent to NBCOT a few days after graduation. After that, I received my authorization to test (ATT) letter from NBCOT within a week, and chose my exam date within about 2 weeks following graduation.
This may be different for some schools and I know that there are some situations in which you can apply to take the exam before graduation (such as in an OTD program).
Hope that helps.