How to properly Quit a Contract Job When Offered Another?

I am currently working a contract position till Oct, Boss is trying to get me extended but he has no promises.

Recently I interviewed for an was accepted for ANOTHER contract 12 months in length with better pay. What is the best way to handle this, outside of giving my two week notice? I gave a verbal offer already but I have not signed anything yet. I assume I should contact my currenct contracters, let them know and then contact the company I am working for.

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