Last Glacial millennial-scale climate variability transitioned through distinct cold stadial and warm interstadial states. Here we use Earth system model simulations to demonstrate that nonlinear self-sustained climate oscillations appear spontaneously within a window of glacial-level atmospheric CO2 concentrations (~190–225 parts per million). Outside this window, the system remains in either quasi-stable cold low CO2 or warm high CO2 states, with infrequent and abrupt random transitions driven by noise. In the oscillatory regime, the time between climate transitions is governed by temporal variations in the state of the ocean, atmosphere and sea ice, with CO2 acting as a control on the relative rates of the internal forcing and feedback in the system. The Earth system model results map perfectly to a slow–fast dynamical systems model, where the fixed point of the system transitions into the oscillatory regime through a loss of stability at two critical tipping points, the window boundaries. The deterministic component of the oscillations is modified by a stochastic element associated with internal climate variability. Agreement between observations and the hierarchically disparate models suggests the existence of an internal stochastic climate oscillator, which tracks variations in atmospheric CO2 level through the glacial, acting in concert with noise-induced transitions.