As someone who still struggles with the same problem, here are some things that really help me:
First, be open about it. Talk about it to your family, friends, colleagues, boss. That way you'll at least get rid of the shame and the guilt that accompany this "handicap". When my teenage kids, who are very sensitive this kind of thing, bug me about my trembling, or my breaking voice (which may come in a variety of social situations), I explain to them that it's not something that I do on purpose, and that it's not something I control.
In fact, when I get this kind of anxiety which is manifested physiologically (which can look scary to the other people in the room), I try to explain to my audience what's happening to me. I have found that people's attitude will change from bewilderment and suspicion to empathy, which immediately lowers the tension in the room, helps me calm down somewhat and lets me get on with the subject matter with greater ease.
I have also found that concentrating on my breath helps tremendously, and in fact the physical effects come because my body muscles seem to contract in a sort of panic reaction, and the only way I can reverse that is to take long, slow breaths that relax my body.
So, when talking in public, I slow down, taking the time to breath at the end of each phrase. This is not easy to do at first, but combined with an attentive and empathetic crowd, it really changes everything! A practice that I have found to work really well, is to practice mindful breathing while doing some activity, like programming, cooking, gardening or whatever.
I found this to be surprisingly challenging at first, as you need to split your attention between the activity at hand and the controlled slow breathing. But every time I practiced it (especially in preparation for giving a talk), the difference was remarkable.
I hope this helps!