Nick,
Congratulations on the offer.
Would you "need" to take the job if your current company offered you the same salary/pay? If so, then do the "honorable" thing to do is to give them 2 weeks (or maybe longer if the new company will agree to it) and bust your ass to finish what you can. If not, then give your current company the opportunity to match the offer and make your decision to leave or stay based on their decision.
Good luck,
Parker Boy