First of all, there are two main schools of thought regarding ‘intention’ to kill the Jews. Intentionalist historians believe that Hitler always planned to kill the Jews – in January 1939 he spoke about another world war which would lead to the “...annihilation of the Jewish race in Europe!”. Functionalist historians believe that the Final Solution was a consequence of the competitive and sometimes volatile nature of Nazi bureaucracy – it was not premeditated, and, instead, other plans to evacuate and resettle European Jews were a priority before 1941.
Some links:
Wikipedia – Functionalism versus Intentionalism
Part of Lecture series – ‘Was the Holocaust planned or premeditated?
Although the Wannsee Conference in January of 1942 is usually regarded as the official 'start' of the Final Solution, it is likely that the Nazis intended to kill Jews en masse before this. Depending on interpretation of sources and testimony, there's evidence of plans for deliberate annihilation from the beginning of 1941, a year before the Wannsee Conference (which was delayed anyway, as it was meant to occur in December of '41).
First port of call – January 1941. In Erich von dem Bach Zelewiski’s testimony from the Nuremberg Trials, he refers to Himmler speaking of 30 million people who must disappear in the East.
Link to testimony here, scroll down to 7 Jan ‘46
As you can see in the link, the direct wording is, “... he spoke of the purpose of the Russian campaign, which was, he said, to decimate the Slav population by 30 million...” So Himmler was apparently referring just to Slavs and not to Jews – but is it reflective of intent to commit mass murder as early as January 1941?
In March of 1941, Hitler called for th invasion and defeat of the Soviet Union. Because of the links made between Jews and Bolsheviks – Judeo-Bolshevism – some historians (Hillgruber) believe that Hitler implicitly asked for the annihilation of Jews when he called for the downfall of Bolshevism and the Soviet Union. Again, this depends on your interpretation of sources – how much did Hitler expect his audience to “read between the lines”?
For Operation Barbarossa, four Einsatzgruppen commandos were created. Their job was to kill civilians, and, of course, they were eventually responsible for the mass murder of thousands of Jews. Some post-war testimony suggests that the Einsatzgruppen had been instructed to murder Jews before the invasion on June 22 1941:
“At this time we were already being instructed about the tasks of exterminating the Jews. It was stated that Eastern Jewry was the intellectual reservoir of Bolshevism and, therefore, in the Fuhrer's opinion, must be exterminated..” Einsatzgruppen Reports, p.VII
Obviously there are problems with testimony obtained after the war, especially if no records exist of meetings like the one discussed above. In terms of documentary evidence, there is a letter from Heydrich dated 2 July 1941 which details orders for the Einsatzgruppen to kill Jews in party and state employment, as well as other political officials and administrators. Documents on the Holocaust: Selected Sources on the Destruction of the Jews of Germany and Austria, Poland, and the Soviet Union, pp. 377-378.
Following this came orders to focus on Jewish civilians. On the 28th of July, the order came from Himmler that “All Jewish men should be executed, and the women and children pushed into the swamps” (I googled this quote and found lots of sources, so you can do the same – I’ve gotten it from a Holocaust Source Booklet issued by Yad Vashem). By the end of July, orders for a preparation of a final solution have begun. (Documents on the Holocaust, p233)
So, in terms of your question – well, sometime in 1941, well before the Wannsee conference, probably around summer, the Nazis decided to murder a large number of Jews.
You also might be interested in reading through some of the docs on this page: Statements by Leading Nazis on the “Jewish Question”