Atrial fibrillation (AF) is the most common cardiac arrhythmia and currently affects more than 650,000 people in the United Kingdom alone. Catheter ablation (CA) is the only AF treatment with a long-term curative effect as it involves destroying arrhythmogenic tissue in the atria. However, its success rate is suboptimal, approximately 50% after a 2-year follow-up, and this high AF recurrence rate warrants significant improvements. Image-guidance of CA procedures have shown clinical promise, enabling the identification of key patient anatomical and pathological (such as fibrosis) features of atrial tissue, which require ablation. However, the latter approach still suffers from a lack of functional information and the need to interpret structures in the images by a clinician. Deep learning plays an increasingly important role in biomedicine, facilitating efficient diagnosis and treatment of clinical problems. This study applies deep reinforcement learning in combination with patient imaging (to provide structural information of the atria) and image-based modelling (to provide functional information) to design patient-specific CA strategies to guide clinicians and improve treatment success rates. To achieve this, patient-specific 2D left atrial (LA) models were derived from late-gadolinium enhancement (LGE) MRI scans of AF patients and were used to simulate patient-specific AF scenarios. Then a reinforcement Q-learning algorithm was created, where an ablating agent moved around the 2D LA, applying CA lesions to terminate AF and learning through feedback imposed by a reward policy. The agent achieved 84% success rate in terminating AF during training and 72% success rate in testing. Finally, AF recurrence rate was measured by attempting to re-initiate AF in the 2D atrial models after CA with 11% recurrence showing a great improvement on the existing therapies. Thus, reinforcement Q-learning algorithms can predict successful CA strategies from patient MRI data and help to improve the patient-specific guidance of CA therapy.