Or you can get a true SoC FPGA, like Xilin's Zynq, Altera's Cyclon V SoC, or Microsemis' FPGAs (many have ARM cores inside).
Basically, they have an ARM core, or multiple, A9, or M0. You can watch that explain why you should use SoC+FPGA, and obviously, the whole thing is to try to sell you Altera's... But anyways, I think it gives you a good enough understanding on the thing...
One problem is price... those chips are expensive, and the development boards are not cheap either.