So, as my username might suggest, I am quite familiar with Austrian history. I have written and researched about this before, so I will try to summarize what I've learned as well as provide some archival and secondary sources so that you can continue to do your own research if you want!

First, it's important to note that Austria was not "reunified" in 1955, but rather regained independence and autonomy from the Allied Powers, with the last occupiers leaving, in 1955. Before this, they had been under the unified administrative powers of the Allied command, with separate administrative zones for the British, American, French, and Soviets, much like Germany.

However, they were able to regain this independence and remain one unified country in 1955 for several reasons. First, the myth of Austria as the "Nazis' First Victim" stacked the cards in their favor even before the war was over. Second, immediately following the war, the Austrians proclaimed their intention to become a neutral power within the emerging Cold War, citing the example of the Swiss in WWII and after. Lastly, they demonstrated a remarkable ability to cooperate within the political system, showing that they would be able to overcome the political divisions that the international community agreed had largely led to the Nazi takeover.

In 1938, Germany "invaded" Austria, adding its territory on the basis of the ethnic German majority. This would come to be known as the Anschluß. While some people called the Anschluß an invasion, for many it was the natural progression of history. It had followed a long history of nationalistic attempts to unify the two lands. However, before WWI, the inclusion of the other territories in the Habsburg Monarchy caused problems with such a unification (for more information on this, look up the Großdeutsch and Kleindeutsch solutions). After World War I, the forced breakup of the Habsburg Monarchy left rump Austria, with by far a greater amount of ethnic Germans, ripe for the picking. (It is worth noting that much of the nationalistic rhetoric that led to the Anschluß was based on false identity politics, which painted a picture of stark nationalistic identities with the Habsburg Monarchy, when, in fact, such divisions were not nearly as clear cut or, in many cases, did not exist at all.)

After the war, the Austrian leaders were able to use the Anschluß to legitimize their authority. They overlooked the overwhelming support for the Anschluß and, as Tony Judt argues, collectively "forgot" their involvement in WWII. This allowed them to move on from the war and establish a government free from the legacy of the Nazis. They would not really examine or come to terms with this legacy until the Haider Controversy in 1990.

Free from the onus of their Nazi participation, the Austrians were able to proclaim their intent to become a neutral state (joining, the so-called 3rd World, in opposition to the 1st World of the Americans and the 2nd World of the Soviets). Much of the discussions with the Soviets and the Americans after the war - by far the biggest players in the peace talks - centered around the proclamation of their neutrality. They believed that the Austrians could and should follow the example of their "Swiss brothers" in this regard.

To demonstrate that they would be able to complete this feat, the political parties of Austria were able to put aside their differences and show that they could cooperate with each other, effectively ending what they believed was the destructive political partisanship that had torn their country apart even before WWII. The archival sources that I have looked at are full of these discussions of cooperation between previously antagonistic parties. They knew that in order to become neutral and get out from under Allied Occupation, they had to cooperate; and so they did.

After many years of negotiations, with the various geopolitical parties engaging in long and protracted dialogues, often shifting due to other political problems in Europe and elsewhere, Austria was finally able to conclude their treaty with the Allied Powers. The terms of this included that Austria would be neutral in return for having all of the occupiers leaving and remaining whole. On October 25, 1955, the last of the occupiers left, finally handing over the last bits of control to the Austrian government.

Sources:
Archival
General Records, 1945-1952, Office of the US High Commissioner for Austria and Office of the Political Advisor (HCA), Records of the Foreign Service Posts of the Department of State, Record Group 84 (RG84), National Archives and Records Administration – College Park, MD (NACP).

Classified Records, 1945-1955, HCA, RG84, NACP.

Top Secret Records, 1945-1955, HCA, RG84, NACP.

Public Opinion Studies and Surveys, 1950, HCA, RG84, NACP.

19th and 20th Century Newspapers in Original Format, Library of Congress, Washington, D.C.

Secondary
Bischof, Günter. Austria in the First Cold War, 1945-55: The Leverage of the Weak. New York: St. Martin’s Press, 1999.

Carafano, James Jay. Waltzing into the Cold War: The Struggle for Occupied Austria. College Station: Texas A&M Press, 2002.

Judt, Tony. Postwar: A History of Europe since 1945. New York: Penguin Press, 2005.

Lewis, Jill. Workers and Politics in Occupied Austria, 1945-55. New York: Manchester University Press, 2007.

Liebhart, Karin. “Transformation and Semantic Change of Austrian Neutrality: Its Origins, Development and Demise,” in Neutrality in Austria: Contemporary Austrian Studies, Volume 9, Günter Bischof, Anton Pelinka, and Ruth Wodak, eds.: 7-36.

Luif, Paul. “Austria’s Permanent Neutrality – Its Origins, Development, and Demise,” in Neutrality in Austria: Contemporary Austrian Studies, Volume 9, Günter Bischof, Anton Pelinka, and Ruth Wodak, eds.: 129-159.

Pick, Hella. Guilty Victim: Austria from the Holocaust to Haider. New York: I.B. Tauris & Co. Ltd, 2000.

Rathkolb, Oliver. The Paradoxical Republic: Austria 1945-2005. New York: Berghahn Books, 2005.

Stiefel, Dieter. Entnazifizierung in Österreich. Vienna: Europaverlag, 1981.

Utgaard, Peter. Remembering and Forgetting Nazism: Education, National Identity, and the Victim Myth in Postwar Austria. New York: Berghahn Books, 2003.