Atomic-level qubits in silicon are attractive candidates for large-scale quantum computing; however, their quantum properties and controllability are sensitive to details such as the number of donor atoms comprising a qubit and their precise location. This work combines machine learning techniques with million-atom simulations of scanning tunnelling microscopic (STM) images of dopants to formulate a theoretical framework capable of determining the number of dopants at a particular qubit location and their positions with exact lattice site precision. A convolutional neural network (CNN) was trained on 100,000 simulated STM images, acquiring a characterisation fidelity (number and absolute donor positions) of >98% over a set of 17,600 test images including planar and blurring noise commensurate with experimental measurements. The formalism is based on a systematic symmetry analysis and feature-detection processing of the STM images to optimise the computational efficiency. The technique is demonstrated for qubits formed by single and pairs of closely spaced donor atoms, with the potential to generalise it for larger donor clusters. The method established here will enable a high-precision post-fabrication characterisation of dopant qubits in silicon, with high-throughput potentially alleviating the requirements on the level of resources required for quantum-based characterisation, which will otherwise be a challenge in the context of large qubit arrays for universal quantum computing.