The supplement to Hitler's Fuhrer Directive 33, Fuhrer Directive 33a, issued on 23 Jul 1941, stated:
"The enemy forces which are still west of the Dnieper must be
decisively defeated and dispersed. As soon as the state of operations
and supplies allows, First and Second Panzer Groups will be
concentrated under command of Fourth Panzer Army and, with the support
of infantry and mounted divisions, will occupy the Kharkov industrial
area and thrust forward across the Don to Caucasia."
So German plans for operations in the Caucasus and Middle East clearly predate Japan's entry into the war, but there can be no doubt that in addition to the obvious economic importance of the move, there was anticipation of diplomatic benefits as well. After Japan's entry into the war Hitler saw this strategy as one which was in accord with his ideas for greater co-operation between the Axis powers.
Map from 'War Maps: Great Land, Sea, and Air Battles of World War II', S. Goodenough
On 3 January 1942, Hitler met the Japanese ambassador, Oshima, to discuss his future plans and co-operation between the two powers. Specific links were made between the intended German strategy and possible political ramifications in the Arab world, as well as broader mention of shared German and Japanese strategic interests in the fate of Russia and India. A German observer of Hitler's meeting with Oshima noted:
...For the time being he did not intend to carry out any more attacks
in the centre of the front. His goal was an offensive on the southern
front. Picking up the thread of his argument again, the Fuhrer
declared that he was determined to take up once again the offensive in
the direction of the Caucasus as soon as the weather was favourable.
The thrust in this direction was the most important one: we must get
to the oil and to Iran and Iraq. Once we were there, he hoped that we
could get help to unleash the freedon movement of the Arab world.
Naturally, in addition, he would do everything possible to destroy
Moscow and Leningrad.
...All of us and Japan as well were engaged in a joint life and death
struggle and so it was vital that we share our military experience.
...[Hitler then] emphasized that it was probably the first time in
history that two such powerful military powers, which were so far
apart from one another, stood together in battle. Provided their
military operations were co-ordinated, this offered the possibility of
creating leverage in the conduct of the war which must have enormous
effects on the enemy, since they would be thereby compelled
continually to shift their centres of gravity and in this way would
hopelessly fritter away their forces. He did not believe the United
States would have the courage to conduct offensive operations in the
East Asian sphere... the Fuhrer continued "if England loses in India a
world will collapse. India is the cornerstone of the English Empire.
England acquired all its wealth from India".
...The Fuhrer is of the opinion that England can be destroyed. He is
not sure yet how the USA can be defeated. The South American states
would, in his opinion gradually move away from the United States. In
reply to a comment by the Foreign Minister [Ribbentrop] that Japan
might be in a position to attack Russia in May, the Fuhrer said that
the most important thing from Germany's point of view was that Japan
was not defeated by the Anglo-Saxon powers. It must not prematurely
dissipate its forces. For us too England was the main enemy. We would
certainly not be defeated by Russia. He pointed out to Oshima the
long-term danger of the United States and England establishing
themselves in a big way on the Australian continent. Oshima is of the
same opinion and convinced that Japan would soon secure bases in
Australia. In addition, it was obvious that Japan must one day beat
Russia, for otherwise the new order in East Asia would be impossible.
At the moment, she was still heavily committed with her troops in
China. However, he was convinced that the Chungking government would
get progressively weaker in the coming months and then Japan would be
in a position to withdraw troops from China.
Roosevelt's greatest mistake was to impose sanctions on Japan without
at the same time being sufficiently well-armed. This was a really
crazy policy. The Fuhrer was of the same opinion and said that if one
did not want to wait until one's throat was cut one simply must strike
first and Japan had correctly recognized that and done it. The Fuhrer
is of the opinion that it is extremely important for Japan and Germany
to exchange their military inventions. Germany has no interest in East
Asia and Japan none in Europe and Africa...
On 18 January 1942, the diplomatic agreement between the Axis powers of 11 December 1941 was supplemented by a military one. According to this, the world was divided into two zones of military operations along the line of 70 degrees longitude, with Japan being responsible for the area east of the line, and Germany and Italy for that west of it.
Source: Nazism 1919-1945: vol.3: Foreign Policy, War and Racial Extermination (A Documentary Reader), edited by J. Noakes and G. Pridham (1997)