I have received a written offer. The new employer and I have both signed the written offer yesterday. The employer made a comment (before giving me the written offer) regarding how the start date may be in 2.5 weeks, but have not yet confirmed the exact start date. I communicated to them then that I will be giving my two weeks notice to my former employer once I sign the written offer.
However, I have just completed the background check and have not yet taken the drug test (has not arrived yet)... so I don't exactly feel comfortable giving my two weeks notice just yet, even though I know I will pass (but just in case?).
Anyways, my question is 1) Is is appropriate to ask my new employer to confirm with me when I should give my two weeks notice, since they'll be the ones receiving my background check and drug test results (what's the best way to ask) and 2) When is it appropriate to give my two weeks notice (like what if I don't get my background check and drug test results within the next week, if I wait to have the results, I may not have enough time to give my two weeks notice to my former employer, which means I may not be able to start in 2.5 weeks...?)