The philosophical doctrine that free will and determinism are compatible. This viewpoint is the opposite of incompatibilism.
Most compatibilists are also soft determinists. That is, they believe that determinism is true and free will exists. (I, personally, am sort of a soft determinist as I tend to believe is determinism is true, but I don't believe there is a conclusive logical argument that proves this is so.) Compatibilists also generally believe that indeterminsm and free will are incompatible.
To many incompatibilists, compatibilism seems obviously self-contradictory because free will is generally thought to require indeterminism by definition. One response is that free will actually requires determinism in order to make sense because indeterministic choices would be arbitrary, not free. Another response is that indeterminism and "could have chosen otherwise" are not essential aspects of the concept of free will. Indeterminism is something that most people think of as requirement for free will to exist, but that does not mean it is really part of the definition.
David Hume is the first compatibilist in the history of philosophy that I know of. In modern times, R. E. Hobart's 1934 essay, "Free Will as Involving Determination and Inconceivable without It" is the major compatibilist work that most other compatibilist's reference. Daniel Dennett is the most prominant present-day compatibilist. He defends his position in his 1984 book, Elbow Room: The Varieties of Free Will Worth Wanting.
Edit: DrRetard informs me that Thomas Hobbes was a compatibilist before David Hume.