There just wasn’t any pragmatic reason to remain antagonists anymore for the Austrians and the Ottomans.  The time of the Ottomans rivaling Austria for had been finished for a long time by the start of the Great War.  They weren’t even close to sharing the same geographic space anymore.  Serbia gained de facto independence (as a much smaller state than today or even 1914) in 1867, and gained recognition at the Congress of Berlin in 1878, which is when Austria gained de facto control of Bosnia (officially annexed 1908).  Montenegro had been recognized in 1852.  Romania officially broke away at the previously mentioned 1878 Berlin treaty, though Ottoman control had been nominal at best since the end of the Crimean War in 1856.  Bulgaria also escaped de facto Ottoman control in 1878, an independence that was merely formalized in 1908.

Greece of course did its thing in 1832. So by 1914 Austria and the Ottomans hadn't been a "thing" for over 40 years. Austria v Russia had been the thing in its place, vying for dominance in the new Balkan ball pit. Even in the wildest "Mitteleuropa" dreams of Vienna they would never need to encroach on the new Ottoman sphere, especially not after the Balkan Wars where the Ottomans lost nearly everything northwest of Constantinople.

Further, the Ottomans had lost territory in the Caucus region to Russia in the century before the Great War, they had lost Libya to the Italians in 1911 with the approval (either explicit, as with the French, or implicit as with the British) of Germany's enemies, and Britain had ruled Egypt de facto since 1856 in what was certainly a humiliating arrangement for the Ottomans.  On the other hand, Turkish relations with Germany had been developing since the Berlin Treaty, where Bismark stunted Ottoman losses in the preceding war with Russia. 

So there was great pragmatism is the arrangement. 

Austria's enemy was Russia and Russian client states, which at the time meant Serbia and Romania (although Romania had been an Austrian ally until the start of the war and Serbia had been an Austrian ally until the brutal murder of the royal Obrenovic family in 1903). Austria also allied with Bulgaria, which has previously been Russia's most powerful and important client until 1913, when Russia betrayed them in favor of Serbia during the Balkan Wars. 

Their war goals weren't incompatible either. The Ottomans could hope that a German victory would bring them land recoveries in the Caucasus at the expense of Russia, the recovery of Egypt from the British, and/or the expansion of influence into British middle east and Persia. The Italian entrance to the war opened the door to recovering Libya. The Austrians had extremely limited territorial goals in the early stages, either hoping for no annexation or limited annexations of northern Serbian lands. Victory for Austria would look like, well, victory but also survival and the reduction in Russian influence in the region not territory. 

So it was merely an alliance of pragmatism. It wasn't universally popular, either. There were strong arguments that the Turks should join the allies, partly based on the fact that the Ottomans had been forced to surrender large tracts of government administration to the French due to their financial troubles and maybe France would be willing to be generous in the matter if the Ottomans joined the Allies. Their were also people in the Austrian ranks who weren't totally sold on dealing with their old school rival, but the value of distracting Russian and British troops on new fronts plus the critical strategic value of denying the Black sea as a logistics channel for Russia was just too high to turn away in the end.