Temp to Perm Job Transition Etiquette

Quick background: I’ve been working a temp position at a hospital in Los Angeles for the past 18 months. A permanent position with my present job title at the hospital has finally opened and I applied last week. If I get the position, this would be my first time converting from temp to perm. If I’m successfully hired (which was essentially guaranteed by both of my supervisors), what do I tell my temp agency? Do I need to give two week’s notice? Since the new position is technically my contracted position, would there be a handoff between the temp agency and my job that I should be aware of? Or can I just announce my exit from the temp agency the same day I submit my last timesheet?

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