On his website Gordon Napier published an elabroate and apparently well researched review of the Masters of the Knights Templar through the ages. This review was an adapted version of A to Z of the Knights Templar by the same author. This blog quotes in full the introduction to this review with some minor adaptations.
"The Grand Masters were the leaders of the Knights Templar. The Hospitallers were also under a Grand Master, as were other Military Orders (the alternative term Grand Prior was sometimes used by the Hospitallers, and the term 'General Master' was also used). The leader of the Teutonic Knights was called the Hochmeister. The Term 'Grand Master' does not appear in the Templars' original rule (only 'Master') but it s generally understood to refer to the Order's leader.
The Grand Master was the spiritual, political and military leader of the Order. He was chosen by a complex electoral system similar to that used in Venice to elect the Doge. The Preceptors in the Holy Land would usually choose a provisional leader until an electoral college, drawn from the international Order's chapters, could be established. Eventually after a whittling down process, the next Grand Master, who was in theory supposed to be an experienced, professed brother of the Order, and not a partisan outsider. The Grand Master was supposed to be beyond the influence of Kings, and to answer only to the Pope. The Grand Master presided from Jerusalem. After the fall of Jerusalem in 1187 the main town became Acre. After the fall of Acre in 1292 the Order was presided from Cyprus.
Read the whole review by Gordon Napier here.