What pretext did Hitler use to justify Operation Barbarossa?

Radio broadcast to the German people

Hitler gave his reasons to the German people via a radio broadcast on the morning of June 22nd, 1941.

At 0500 GMT, an hour after the invasion began, the Nazi Minister for Propaganda, Joseph Goebbels, went on national radio to read a proclamation by Adolf Hitler

The proclamation can be seen here in full. Basically, Hitler argued that the Soviets were a threat to Germany and had broken the peace. Thus, Germany was 'forced' into a preemptive strike:

...the invasion was presented as a pre-emptive defensive move that the Wehrmacht leadership had to undertake in order to avert a Soviet attack on the Reich...

Source: Aristotle A. Kallis, Nazi Propaganda and the Second World War (2005)

He also railed against the threat posed by 'Jewish-Anglo-Saxon warmongers'. Below are some excerpts for those who (understandably) don't wish to wade through the entire proclamation:

...Moscow not only broke our treaty of friendship, but betrayed it!

I was forced by circumstances to keep silent in the past. Now the moment has come when further silence would be not only a sin, but a crime against the German people, against all Europe.

Today, about 160 Russian divisions stand at our border. There have been steady border violations for weeks, and not only on our border, but in the far north, and also in Rumania. Russian pilots make a habit of ignoring the border, perhaps to show us that they already feel as if they are in control.

During the night of 17-18 June, Russian patrols again crossed the German border and could only be repelled after a long battle.

Now the hour has come when it is necessary to respond to his plot by Jewish-Anglo-Saxon warmongers and the Jewish rulers of Moscow’s Bolshevist headquarters.

There was no build-up propaganda prior to the invasion - after all, why give the Soviets any hints? On the contrary, German propaganda focused on attacking Britain.

The absence of any reference to Bolshevism, Stalin and his empire, even for the purpose of negative integration or diversion from the evident failure of the regime’s anti-British strategy, had been conspicuous in the output of NS propaganda for a while – and it remained so until 22 June 1941, that is after the start of the war in the east....Although the time of the invasion of the Soviet Union was drawing near, Goebbels continued to deceive not just public opinion but everyone involved in the dissemination of information.

Source: Kallis

Attacks on Bolshevism had essentially ended with the 1939 non-aggression pact but were now renewed, bundled together with anti-semitism in a

‘Jewish–Bolshevik–plutocratic’ conspiracy

with the added ingredient of Germany protecting Europe's "civilization and history".

German public's reaction

How much of this the public believed or felt justified the invasion is hard to determine. Kallis suggests that the public was wary at first of taking on such a large opponent but, when reports came in of a series swift victories, attitudes changed. The article Attack on Russia cites the recollections of one German girl:

Maria Mauth, a 17-year-old German schoolgirl at the time, recalled her father's reaction: "I will never forget my father saying: 'Right, now we have lost the war!' " But then reports arrived highlighting the easy successes. "In the weekly newsreels we would see glorious pictures of the German Army with all the soldiers singing and waving and cheering. And that was infectious of course...We simply thought it would be similar to what it was like in France or in Poland – everybody was convinced of that...

This new optimism of a quick victory didn't last, of course.

Letter to Mussolini

In a letter to Mussolini, dated June 21 1941 (i.e. before the invasion began), Hitler outlines many of the same reasons, emphasizing his belief that the Soviets had to be dealt with as

...with so gigantic a concentration of forces on both sides—for I also was compelled to place more and more armored units on the eastern border, also to call Finland's and Rumania's attention to the danger—there is the possibility that the shooting will start spontaneously at any moment.

Interestingly, Hitler does not attempt to fool Mussolini with the claim (made in his radio broadcast) that the Soviets had been provocatively attacking German positions along the border.

Other related links

German Foreign Minister Joachim von Ribbentrop text justifying war against Soviet Union

Soviet response: Radio speech by Molotov 22-06-1941 in which he lays the blame specifically on the 'Fascist German rulers' rather than the German people:

This war has not been forced on us by the German population, nor by the German workers, farmers and the intelligentsia, whose suffering we understand very well but by a clique of blood thirsty, Fascist German rulers who have suppressed the French, Czechs, Poles, Serbs, Norwegians, Belgians, Danish, Dutch, Greeks and other peoples.