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In the outer solar system, the Kuiper Belt contains dynamical sub-populations sculpted by a combination of planet formation and migration and gravitational perturbations from the present-day giant planet configuration. The subdivision of observed Kuiper Belt objects (KBOs) into different dynamical classes is based on their current orbital evolution in numerical integrations of their orbits. Here we demonstrate that machine learning algorithms are a promising tool for reducing both the computational time and human effort required for this classification. Using a Gradient Boosting Classifier, a type of machine learning regression tree classifier trained on features derived from short numerical simulations, we sort observed KBOs into four broad, dynamically distinct populations - classical, resonant, detached, and scattering - with a >97 per cent accuracy for the testing set of 542 securely classified KBOs. Over 80 per cent of these objects have a $>3σ$ probability of class membership, indicating that the machine learning method is classifying based on the fundamental dynamical features of each population. We also demonstrate how, by using computational savings over traditional methods, we can quickly derive a distribution of class membership by examining an ensemble of object clones drawn from the observational errors. We find two major reasons for misclassification: inherent ambiguity in the orbit of the object - for instance, an object that is on the edge of resonance - and a lack of representative examples in the training set. This work provides a promising avenue to explore for fast and accurate classification of the thousands of new KBOs expected to be found by surveys in the coming decade.