Acceptance With Grace. The best_case scenario__and honestly, the most common reaction__is that your boss will accept your resignation with understanding and sincere congratulations. Your manager will be happy to see that you're advancing your career and moving on to something bigger and better.
However, at most companies, there's no formal requirement that you do so. Most employment in the United States is called "at will", which means that your current employer can fire you at any time and for any reason (except those that are prohibited under law).