It was during the reign of Selim II, the son of Suleiman that Armenia became a province in the Ottoman Empire. Little incidents in history have the power to modify it for good or bad and the Armenian chapter in the Empire's history was also something similar. Armenia would become an important part later on because of the mass genocide that made it known to the world for wrong reasons.
3 centuries of rule under the Ottoman Empire and the Armenians had proved key players in the political and military stability of the region. As recent as the World War I, Western Armenia was still under the rule of the Ottoman Empire after which the downfall of the Empire as a whole resulted in Armenia gaining freedom. One striking feature of the political system of the Ottoman Empire was - like Islamist doctrines, the state did not differentiate between religious and political powers.
That is, the religious heads had as much a say in the state of affairs as the Sultans did. The structural rigidity that came to be defined later on in the history of Ottoman Empire was nonexistent at the time when Armenia was ceded to the same (1524-1574) - and this was one of the reasons as why Armenia was integrated into the Ottoman Empire.
Armenia - Byzantine, church and Constantinople
To understand the annexation of Armenia to the Empire, it is important to understand the series of events that in turn tilted the scales in favor of the Empire to annex the region under its umbrella. The Byzantine Church was not in favor of Armenians coming to Constantinople because the Armenian Church was seen as heretical. Ecumenical Patriarchate of Constantinople saw the rise of Armenians as religious leaders and bureaucrats and began playing an important role in the Ottoman administration.
Armenians though were mostly villagers were quite prosperous; sometimes more than the city people of the Ottoman Empire. Perhaps their way of living and culture prompted the sultans to annex the region under its control. The Ottoman Turks were the ones who facilitated the integration of Armenia.
Armenians in the Ottoman Empire were not suppressed and largely preserved their school of thought and religious policies because of the fact that they shared a lot on similar with the Kurds and Turks of the Empire. The notable evolution of the Ottoman Turks in 3 distinct Millets are - the Armenian Orthodox Gregorian, Armenian Catholics, and Armenian Protestants - which came into existence in the 19th century.