The best scenario is that you will have a few clients drop out, but the increased rate will keep you income the same. You may also gain a few new clients as well. The best thing is to be direct and honest, tell them what you plan to do and give them time to decide.
If you write them a letter, make it short and to the point, and explain to them what you plan to do. You do not have to give reasons why, because that is unimportant and does not pertain to them. All they are interested in is what the new rate will be and when it will take effect. Another thing to consider, since therapist and client relationships tend to become less formal with regular clients, make the letter more formal than how you usually speak to them. A formal sounding, simple business letter is the best way to do it.