A tubular racking system has a racking module connected to a drilling rig mast. The racking module has a frame, a fingerboard assembly, and a clasp extendable to a stand hand-off position for securing a tubular stand in position. An upper racking mechanism (upper racking mechanism) has a bridge translatably connected to the frame. An arm is rotatably and translatably connected to the bridge. A gripper is translatably connected to the arm. A setback platform module has a platform and an alleyway adjacent the platform. A lower racking mechanism (lower racking mechanism) is translatably connected to the alleyway. The lower racking mechanism is rotatably and extendable with a clasp operable to secure a tubular stand from horizontal movement. Movements of the lower racking mechanism are controlled by movements of the upper racking mechanism.