The first thing you should do is look at the answer to this question. Then realize that this is not an issue, but something that you can use greatly to your advantage. However, you still have the problem of not having your own style. I will address that below.
I am a natural mimic as well. When I started out writing, I wrote like whatever I read. I was writing and reading frequently enough and at the same time, so that my style eventually became a collection of different mimics. Or so I thought.
As a mimic, you are going to adopt the style of several authors into your own style. This is just how it works. But as an individual person with a distinct personality and life, those styles are also going to be shaded over by your own experiences and beliefs. This is also how it works.
As my writing style solidified, I found that it was slipping into a different groove. There were elements taken from C. S. Lewis and Edith Nesbit, along with Eoin Colfer and G. A. Henty. But there was something else in there, something that was purely me. That something wasn't my style. But it was what made my collection of mimicked styles different.
So the second thing you need to realize is that 'your style' is a collection; a collection of mimicked styles from authors you love, coupled with who you are. This style will emerge naturally, as long as you just keep writing, and don't worry about it.
That being said, there is an exercise you can do to bring your own unique style closer to the forefront of your writing. The first step is to stop reading, at least for a little while. Take a month off, and at the end of that month (don't start reading!) write. (As a writer, you should never stop reading entirely. A month is okay.)
The second step is what you write. Don't write just anything. Write something you really believe in. Find a topic that is close to you, some position you would defend if it was questioned by someone else. Do you have something you genuinely believe other people need to know? Good. Write about it.
Why am I doing this? By writing about what you believe in deeply, you're pulling from who you are. You're pulling from your experiences, what you know, and how you feel. Coupled with having not read a book recently, you will be unable to stop your own style from pouring out. Then, later, whenever you want to write in your own style, simply re-read what you wrote, and use your mimicry to your advantage.
It should be noted that this will only work if your style is not yet solidified. If it is, your style has become a part of you and you will write that way no matter what. This is a good thing though, as it means what you read will no longer cause your writing to fluctuate quite so drastically. You can still mimic if you focus on trying to, so you haven't lost that ability either.
Best of luck!