Short answer: it is a result of the presence and activities of the Teutonic Order during the Northern Crusades and its ties to Germans as such. Now, let's go for the long answer.

Prussia, more or less corresponding to the lands that now comprise of Warmian-Masurian Voivodeship in Poland, southwestern Lithuania and a Russian exclave of Kaliningrad Oblast was indeed a region that has been inhabited by Western Baltic people and until early 13th century it remained independent, having successfully resisted all attempts of conquest made by their neighbours, predominantly Poland (or Dukedom of Masovia during the provincial division in the years 1138-1320) but also Lithuania, Pomerania, Denmark and Russian principalities. The conflicts were quite intense and the border regions saw significant amount of struggle and instability what caused them to be rather sparsely populated. Similarly, all attempts of Christianization since 970s proved to be unsuccessful.

Large-scale German presence in the Prussian territory that will end only in 1945 due to the territorial cessions decided during the Yalta Conference officially began in the year 1226, when the Masovian duke Konrad I invited the Order of Brothers of the German House of Saint Mary in Jerusalem (commonly known as Teutonic Order), granting them Chełmno (ger. Kulm) area, with the act of beneficium being officially signed in 1228, when the first Teutonic knights arrived in the region. Simultaneously, Order of the Militant Brothers of Christ, formed in 1216 by Bishop Christian of Oliva arrived in Dobrzyń (ger. Dobrin), where he was granted lands by Konrad I.

This decision is largely explained by the Konrad's decision to murder Krystian, voivode of Płock and de facto military commander of all Masovian forces who managed to organize successful network of defences against Prussian invasion and led Polish forces to victory in the Batlle of Zawichost against the invading army of Roman II, prince of Kiev and Galich-Vladimir. It is generally accepted that Konrad I considered Krystian a threat to his position, fearing that the latter might attempt to depose him or help other Polish dukes to take control of Masovia. But Krystian's death meant the collapse of the defence system, encouraging Prussians to continue the incursions Konrad I was unable to stop on his own. Thus, he turned to the Teutonic Order for help. It is worth noting that this was not the first agreement between the Order and the central European rulers. In 1222, Silesian duke, Henry II granted them small holdings in his domain and recommended them to Konrad I, despite the Order's attempt to create their own independent domain in Hungary that resulted in their exile from the country.

Teutonic Order again attempted to take the firm hold of their new lands and this time they managed to get the support of the Holy Roman Emperor and Papal Court. In 1235, Emperor Frederic II issued a document in which he confirmed the Chełmno land as a grant from Konrad I that was defined not as a feudal fief but rather as an perpetual, independent holding, contrary to the actual agreement between Konrad I and the Order. Furthermore, it granted the same status to all potential Prussian lands gained in the future. In the meantime, Militant Brothers of Christ, after several defeats against Prussians, decided to merge with Teutonic Order, significantly increasing their strength in the region. They were followed by the Livonian Order that, weakened by the defeat to Prussians at Saulai in 1236, entered the structure of the Teutonic Order as a semi-independent branch of the Order in 1237. Konrad I, involved in the intensive political struggle with his brothers and other rulers of Polish provinces was unable to counteract, largely leaving Teutonic Order to proceed with the Northern Crusade.

The progress of the Crusade was very fast. Teutonic Order was able to utilize its good organization and support of the Western nobility, Holy Roman Emperor and the Pope, while the lack of political unity between the Prussian nations allowed the crusaders to isolate and eliminate the latter one after another. In addition, Teutonic Order was largely aiming at large-scale colonization rather than simple governance of the newly gained lands, what resulted in exceptionally brutal warfare, often utilizing the unprecedented scorched land tactics. It is generally accepted that the Prussia was completely subjugated by the Order until 1295. Conquest was also followed by quick colonization of the area, predominantly with German settlers, what gradually caused the displacement of the Prussians (often to the lands of their former rivals) and the assimilation of the remaining ones, turning Prussia into chiefly Germanic territory. According to modern estimates, during the Polish-Teutonic war in the early 15th century, native Prussians constituted 35-40% of all inhabitants of the Order's domain (with their percentage gradually increasing north-eastwards, from 20-30% in Pomezania and Bartia to over 90% in Sambia and Natangia). Nevertheless, by that time they were largely culturally assimilated into the Germanic, Christian majority of Prussia. It is estimated that the Prussian language went extinct somewhere around early 18th century.

Now, the Teutonic Oder State, recognized by the aforementioned Golden Bull of Rimini issued by Frederic II in 1235 was governed by the Order that, unlike many other militant chivalric orders, since its origin always maintained strong national ties with German lands and Germanic people. After the conquest of Prussia, Teutonic Order decided to use the political weakness of divided Poland to expand its territory, attacking Pomerania on behalf of duke Władysław I attempting to repel the Branderburgian invasion and keeping the territory for themselves despite papal verdict mandating return of the lands and payment of damages to the Polish duke. In 1327 Order allied with Czech Kingdom and rulers Meklemburg, attacking Poland, but the freshly unified country managed to repel the invaders. This caused the Order to turn against Lithuania, but it only resulted in the alliance between the latter and Poland that eventually led to the emergence of the Polish-Lithuanian Commonwealth. Inability to expand and the Thirteen Years War (1454-1466) led to the Treaty of Thorn, according to which the Grandmaster of the Order and the leader of Teutonic Order State in Prussia became the vassal of the Polish king. In addition, the territory of the Order was divided, with Pomerania, Warmia and Chełmno and Michałów Land (roughly the Western half of the territory, commonly known as Royal Prussia) were returned to Poland and the remaining part (Eastern half, largely composed of former Prussian territories and Livonia) being held by the Order.

Teutonic Order was not really content with the Treaty and attempted to shake of the Polish dominance several times, but after another Polish-Teutonic War of 1519-1521, Grandmaster Albrecht Hohenzollern officially adopted Protestantism, severing his ties with papacy and formally dissolving the Teutonic Order State, turning it to secular Duchy of Prussia. Now, it is worth noting that Hohenzollerns were quite a powerful noble family that essentially ruled the Electorate of Brandenburg. With their relatives ruling in Duchy of Prussia, the family made attempts to consolidate their power what was finally made possible in 1618 after the Duke of Prussia died with no heir, leading to the personal union of Electorate of Brandenburg and Duchy of Prussia. The latter was still a vassal state of Poland, but this changed in 1657, when Polish king Jan II Casimir relinquished his title to these lands in exchange for Brandenburg leaving the alliance with Sweden, at that time being in the state of war with Polish-Lithuanian Commonwealth. Duchy of Prussia was to be returned to Poland in case of the Hohenzollern leaving no heir but this never happened. In 1701, Frederic III, Elector of Brandenburg proclaimed the formation of the Kingdom of Prussia from the territories of Duchy of Prussia (it was possible, as Teutonic Order State and later also Duchy of Prussia never were a part of Holy Roman Empire) what was approved by almost all European powers.