With the start of the protestant reformation, the last grand master Albrecht von Hohenzollern of the Teutonic order converted to Lutheranism and swore fealty to the King of Poland and from 1569 the now Duchy of Prussia was incorporated into the Polish Lithuanian Commonwealth.

How it becomes the property of the Electors of Brandenburg (same dynasty as Albrecht, the Hohenzollerns) invovles a lot of legalese and court intrigue. Albrecht von Hohennzollerns successor Albrecht Friedrich his son had mental health problems. According to custom a fief could be revoked in case of heirlessness or incapacity and the Brandenburg Hohenzollerns convinced the King of Poland to sell them the legal rights to the Duchy's reversion. They also appointed a regent from Berlin and married Albrecht Friedrichs daughter to the son (Johann Sigismund) of the Elector of Brandenburg. With Albrecht Friedrichs death in 1618 his son in law Johann Sigismund inherited Prussia, but it didn't go completely smoothly as he died two years later and Poland tried to legally contest his successors entitlement to Prussia. But the successor of Johann Sigismund, Georg Wilhelm assumed the territory two years later creating a personal union with Brandenburg.

The reason the state that spread from central germany to east prussia became known as Prussia and not Brandenburg (since the rulers main title was elector of Brandenburg) again involves more legal wrangling.

The Hohenzollerns main power base was in Brandenburg, which was part of the Holy Roman Empire (HRE). The Margrave of Brandenburg was also an elector of the HRE. Beneath the Holy Roman Emperor there was only one king, the King of Bohemia. So to circumvent the not being able to declare himself king the elector of Brandenburg agreed with the HRE that he could become King IN Prussia. He was crowned in 1701 in Königsberg, capital of East Prussia today the Russian oblast of Kaliningrad.

It was Frederick II of Prussia who declared himself King OF Prussia after the defeating the Austrians in the first Silesia war but I have to check that I am bit pressed for time.

Sources: Norman Davies, Vanished Kingdoms

Chrishtopher Clark, Iron Kingdom