Müller was a "general with special duties" on the staff of OKH. This made him the top legal officer for the Heer, the German Army, but meant he had no jurisdiction over the Luftwaffe, Navy or SS.
He wrote the first draft of the commissar order, but he doesn't seem to have originated the idea. That happened in a speech by Hitler to a large group (200-250) of senior officers on March 30th 1941, at the New Reich Chancellery. It lasted over two hours, and many of them don't seem to have noticed the instruction to commit war crimes, according to Walter Warlimont's memoirs, although those are often self-serving.
Müller was ordered to produce a draft order on 31st March 1941, apparently by Halder, and his legal adviser, Dr Lattmann, also produced one. These were merged, amended by various people, finally approved by Hitler and circulated by OKW.
It was recognised in OKH and OKW that the commissar order was contrary to international law, and Warlimont at OKW wanted to consider if such a written order was actually necessary. However, it all went ahead.
Müller doesn't seem to have been a priority for individual war crimes prosecution, being treated as a functionary. He was presumably considered part of the "General Staff and High Command" within the first Nuremberg Trial.
Sources: Warlimont's memoirs, and volume IV "The Attack on the Soviet Union," of Germany and the Second World War.