Error budgets are an indispensable tool for assuring that project requirements can be and are being met. An error budget will typically include terms associated with subsystems which are being designed by different teams of engineers, and fabricated by different vendors. It is a useful tool at all levels of design since it provides a means to negotiate design trades in the broadest possible context. Error budgeting is in many ways fundamental to the mission of systems engineering and of course to the overall project success. In this paper we will describe the GMT Adaptive Optics System flow down requirements and their integration with their wavefront error budgets. We will focus on the GMT Adaptive Optics wavefront error budgets for the following observing modes: Natural Guide Star Adaptive, Laser Tomography Adaptive Optics and Ground Layer Adaptive Optics. Finally, a description of the error budgets and the close link between the error budgets and other parameter such as sky coverage, zenith angle, etc., will be discussed in this paper.