At age 14 George Graham became the apprentice to a London clockmaker. After serving a period of seven years in this capacity, Graham was employed by Thomas Tompion (1639-1713), the most prominent horologist and instrument maker of his time.

During his years with Tompion, Graham helped to construct the first machine (later known as an orrery) that would accurately simulate the motions of the planets. Graham assumed Tompion's business upon his mentor's death, and he concentrated his efforts upon designing clocks whose inner workings could prevent or compensate for certain inherent flaws, such as the effect temperature changes had upon the clocks' metal gears. By 1726 Graham had built the mercury-compensated pendulum, as well as the deadbeat escapement, a device whose application allowed clockmakers to design clocks of surprising precision. Graham also invented the cylinder escapement, which allowed wristwatches the same precision as clocks.

As his reputation grew, Graham began to design scientific instruments, never straying from his dedication to unparalleled accuracy. Noting that increased size would allow for greater precision in the study of stars, Graham constructed an 8-ft quadrant for the eminent astronomer Edmond Halley (1656-1742), and he also built a 24-ft zenith sector. Apart from their size, these instruments were notable for the accuracy of the graduations Graham had hand-inscribed upon their faces. His lifelong quest for precision in measurement was recognized by the British Royal Society and the French Academy in 1741 when he was asked to help develop the yard as a standard unit of measurement for both British and French scientists.