How to tell my current employer that I'm leaving?

Question

I have a new job proposal (Software Dev)that just got formal today, they wanted me to start next monday but I asked them to give me a few days, until Wendseday, to talk to my current employer about the situation and to try to finish my current tasks as much as I can in order to avoid leaving the project I'm currently working at unfinished.

The project is impossible to be finished in these time lapse because it is recurrently getting more and more requirements.

I have a good relationship with my current boss, I'm working as an outsource and as a "resource" of this company I can be fired at anytime soon and I've a feeling that was going to happen anytime soon because my boss keeps saying that the company income is not fine right now and that we hope for the best and do our best, etc... Stuff like that

I have no good reason to reject my current job offer and even if the actual company I'm working at offers me more money I wouldn't accept working with them anymore because I'm not part of the company and that is something that is felt daily at the office, people look me like an outcast and even avoid walking nearby me or saying a basic "Hello".

I srsly don't mind that unprofessional behaviour, however I'm done not being taken serious when I have a proposal about making things better in that company as I wasn't hired to do so, I was hired for a single project that keeps getting bigger and bigger because the initial requirement was very poor documented.

Back to the point, should I tell me current boss about this situation today?

Shall I just call my outsource HR and tell them I'm going to resign once I sign my contract with my new employer? (This is my current plan which I consider very unprofessional but who knows maybe I should feel more confident about my thoughts lol)

Will telling my boss about it without telling him that it's a fact that I'm leaving, like making him aware that I may leave and leave once I sign my new contract?

I need advice, thanks for reading my whole tale, your time and perspective is really appreciated.

Answer 1

I am sure there's a canonical question this should be a duplicate of, but the right answer is always:

1. Get a firm written offer in hand from another company (after any negotiation of terms)
2. Accept it, with a defined start date greater or equal to the notice you will provide in step 3
3. Notify your current direct manager and HR rep of what your last day at your current company will be, giving customary notice (2 weeks here in the US, or whatever is contractually agreed or failing that customary in your locale). Doing it in person (or failing that verbally) with your manager is considered polite, but back it up immediately with emailing a signed letter to both parties.
4. That's it. Participate in good faith in information transfer, closing up work, or whatever they want you to do (including stopping coming to work) during your notice period. Usually it is considered a bad move to consider counteroffers to stay at this point.
5. Leave and go to work for the new company. Do not do work for your previous company unless a) you are very well compensated as a contractor and b) your new company/local laws permit such moonlighting.

Under no circumstances do you do any of this different or out of order (except in the extremely unusual case that there are contractual terms preventing it). You do not:

1. Tell anyone at your current company "I'm leaving, no really" before you have accepted a written offer, because they may fire you or jack with you and you are not sure you have employment set up.
2. Give too short notice - the new company knows you're employed and know two weeks is customary. If they balk at you saying "Well of course I need to provide two weeks notice" then they are sketchy and you need to keep looking.
3. Anything else that varies from the sequence above.

This sequence is the norm and it's the norm for a reason. It's expected by employers. It protects your interests maximally. People are always tempted to vary from this to be "nice" or to "convince their current company to change their ways" but if they do they are just being chumps.