You can't prevent resentment, that's up to other people. Whether it's over a billion dollars, or a raise, or a new car, or anything else. The key in most cases is to stop caring so much about what other people think (assuming you're not being an overt jerk to spur the resentment). How highly you value someone's opinion should roughly match how much you value them as part of your life in general; any misalignment of that, will usually cause suffering.

You give it to the Bill & Melinda Gates Foundation. Within reason you could pick a specific project that interests you (education in Sweden, or a specific disease, or clean water in Africa), and they would go after it on your money's behalf. They have the scale and systems in place to do that with large donations.