If you have any desire to continue to work at this company or to return again to work at this company - you don't. Presumably, you knew your own market rate and thought this was the best option to return to a second time, when you came back 3 months ago. And, as a returning employee, you knew much more about what you would be getting into than you did the first time through. I have a hard time believing (and I bet your management will too) that the new offer is so much mind-bogglingly better that you would be crazy not to try it. So... if you give notice this time, be prepared to leave for good.
With that said, if you have really gotten the offer of a lifetime, then give notice, give at least the standard notice, and be short, sweet and polite. At this point, don't expect a counter offer - you literally just renegotiated your salary - it's too soon to reasonably try again. Send a thank you on your last day and head out.