Patient motion due to respiration can lead to artefacts and blurring in positron emission tomography (PET) images, in addition to quantification errors. The integration of PET with magnetic resonance (MR) imaging in PET-MR scanners provides complementary clinical information, and allows the use of high spatial resolution and high contrast MR images to monitor and correct motion-corrupted PET data. In this paper we build on previous work to form a methodology for respiratory motion correction of PET data, and show it can improve PET image quality whilst having minimal impact on clinical PET-MR protocols. We introduce a joint PET-MR motion model, using only 1 min per PET bed position of simultaneously acquired PET and MR data to provide a respiratory motion correspondence model that captures inter-cycle and intra-cycle breathing variations. In the model setup, 2D multi-slice MR provides the dynamic imaging component, and PET data, via low spatial resolution framing and principal component analysis, provides the model surrogate. We evaluate different motion models (1D and 2D linear, and 1D and 2D polynomial) by computing model-fit and model-prediction errors on dynamic MR images on a data set of 45 patients. Finally we apply the motion model methodology to 5 clinical PET-MR oncology patient datasets. Qualitative PET reconstruction improvements and artefact reduction are assessed with visual analysis, and quantitative improvements are calculated using standardised uptake value (SUVpeak and SUVmax) changes in avid lesions. We demonstrate the capability of a joint PET-MR motion model to predict respiratory motion by showing significantly improved image quality of PET data acquired before the motion model data. The method can be used to incorporate motion into the reconstruction of any length of PET acquisition, with only 1 min of extra scan time, and with no external hardware required.