Your premise, unfortunately, is a bit off. The Japanese didn't surrender only to the Americans. In all the major communications and documents it was made clear that surrender was to the Allied Powers. Here is the text of the Instrument of Surrender which lays this out:

We, acting by command of and in behalf of the Emperor of Japan, the Japanese Government and the Japanese Imperial General Headquarters, hereby accept the provisions set forth in the declaration issued by the heads of the Governments of the United States, China, and Great Britain on 26 July 1945 at Potsdam, and subsequently adhered to by the Union of Soviet Socialist Republics, which four powers are hereafter referred to as the Allied Powers.

It was signed Sept. 2nd, 1945, on the USS Missouri by representatives of nine Allied governments.

Now, that being said, there is still an underlying question in play here which does bear a little further discussion. Prior to Soviet entry into the war, the Japanese tried to get the Soviets to play middle-man and bring about a negotiated surrender. I discussed a little about the Soviet-Japanese relations in this previous response, but to expand, during the summer Japan was hoping to use this avenue to prevent being forced into unconditional surrender, but it was a fairly vain hope, as Stalin was less interested in playing peacemaker than he was in 'getting his' and ensuring that the Soviets had an opportunity to chomp off as much territory from Japan as possible. Japanese overtures ramped up with the situation on Okinawa deteriorating, but if anything just helped steel Soviet resolve as they now knew better than ever how weak Japan was feeling. In unofficial meetings with Japanese representative Hirota Koki that June, Ambassador Malik essentially was just slowly stringing Koki along, and there was little interest by the Soviets in either negotiating a renewal of the neutrality pact, let alone assisting in negotiations. With the Potsdam Conference in July, if anything, Stalin's concern was that it might induce Japan to surrender too quickly, and before the meeting, he was looking into how to speed up the timetable for launching the Red Army offensive by over a week.

So anyways, while the technical answer to your question is "They surrendered to both", in answer to the broader one underpinning here, the answer is that they tried, but the Soviets weren't having any of it.

Besides the reasons above espoused you also have to consider previous Japanese-Soviet relationships.

The previous encounter Imperial Japan had with the USSR was the Battle of Kalkhin Gol, in which the entire 6th Imperial Army was basically annihilated (or very nearly so) with the defeat being so significant that it became a major reason for Imperial Japan to inmediately stop all plans to expand into continental Asia and focus on expasion throught the Pacific.

Imperial Japan was also a signatary of the Anti-Commitern Pact and one of the main objectives of the Keipeitai (among other horrible things) was the supression of communism. Do remember that many people still in power was convinced of the idea of communism as a sort of disease that would spread to the country much like Nazi Germany and the Cold War-US conceived communism.

One example of the Axis's view on the Soviet Union and communism was that Hittler stripped Berlin of its "western" defenses and focused them exclusevelly on the "eastern" front defenses, one of the commanding officers going as far as saying "If Im attacked by my rearguard I will consider my job fullfilled".

In fact Tsuyoshi Hasegawa from the Santa Barbara University of California in a recent interview to BBC stated that the reason why Truman launched the Atomic Bombs was to pressure the Japanese to surrender before the Soviets could take more Japanese land (by that point they had already taken the Kuril Islands and were mobilizing for a full invasion of Japan) and that Imperial Japan was in fact, pressured to surrender for fear of the Soviet Union outright annexing them than of fear of the atomic bombs.