The presiding officer of the Society of the Cincinnati, as specified by the Institution, is the president general. George Washington was named the first president general of the Society at a meeting of the founding officers on June 19, 1783, and he was reelected to the office at each general meeting of the Society until his death in 1799. When Alexander Hamilton was elected to succeed Washington in 1800, Martha Washington sent him her husband's Diamond Eagle, which has subsequently been worn by every president general as the official badge of the office.

Seven original members of the Society served as president general in succession until 1847, when the last Revolutionary War veteran to hold the office, William Popham, died. The same year, Henry Alexander Scammell Dearborn, son of Gen. Henry Dearborn, became the first hereditary member to be elected to the position. By tradition, the early presidents general held the office for life; Hamilton Fish was the Society’s longest-serving president general with a tenure of thirty-nine years. Since 1950, each president general has been elected for no more than one three-year term.

Today, the president general is the senior general officer of the Society of the Cincinnati. He presides over its standing committee, board of directors, and executive committee; appoints officials; coordinates the management of the Society’s affairs with the executive director; and serves as the Society’s chief ceremonial official.

The Society has historically collected portraits of its presidents general, which in modern times have often been commissioned by the president’s constituent society. Most of them depict the Diamond Eagle, beginning with the 1840 portrait of Morgan Lewis, the first painting to include the president general’s insignia. These works of art link the Society’s founders to its modern leaders in a tradition of service to their “one Society of Friends.”