About resign

I have worked with the current boss for about 2 years. Unfortunately, I have to move to another state since my LG started a new job there.

Recently I got a job offer in that state, and the paperwork processing is going on. Of course my current boss is not aware of it, since I didn't request reference letter from him. And there is no definition of resign in my initial offer letter. I am a permanent resident now, and have no concern with the visa status.

1. I wonder if It is legal if I give him two-week notice.

2. Do you think I should tell my boss of the new job offer when I resign?

Your input will be appreciated a lot.