We know that Hitler was aware and approved of what was happening in the Soviet Union. The Einsatzgruppen Operational Situational Reports were widely circulated and included the Reichscancellory in their list of receipients. Einsatzgruppen Situational Report 128 of November 2nd, 1941 e.g. was certainly distributed to Hitler. It states:Several retaliatory measures were carried out as large-scale actions. The largest of these actions took place immediately after the occupation of Kiev. It was carried out exclusively against Jews and their entire families. (...) Even though approximately 75,000 Jews have been liquidated in this manner, it is evident at this time that this cannot be the best solution of the Jewish problem. Although we succeeded, particularly in smaller towns and villages, in bringing about a complete liquidation of the Jewish problem, nevertheless, again and again it has been observed in the larger cities that after such an action, all Jews have indeed been eradicated. Further evidence for Hitler ordering the killing of europe's Jews comes from Goebbels in the form of two diary entries. On December 12, 1941 he writes after a meeting of Hitler with the Gauleiter:

As concerns the Jewish question, the Führer is determined to make a clean sweep. He had prophesied to the Jews that if they once again brought about a world war they would experience their own extermination. This was not just an empty phrase. The World War is there, the extermination of Jewry must be the necessary consequence. This question must be seen without sentimentality. We are not here in order to have sympathy with the Jews, rather we sympathise with our own German people. If the German people have now once again sacrificed as many as 160,000 dead in the Eastern campaign, then the authors of this bloody conflict must pay with their lives. http://www.holocaustresearchproject.org/einsatz/situationreport128.html