Respiratory and cardiac motion can strongly impair cardiac PET image quality and tracer uptake quantification. Standard gating techniques can minimize these motion artefacts but suffer from low signal-to-noise ratio because only a small percentage of the total data is utilized. Motion correction approaches have been proposed to overcome this problem but require accurate knowledge of such physiological motion. Here we present a joint PET-MR motion estimation approach which combines complimentary dynamic image information from simultaneously acquired MR and PET to ensure improved cardiac and respiratory motion estimation for motion-corrected image reconstruction (MCIR) of PET images. A 3D triple-echo Dixon MR scan is used both for calculation of MR-based attenuation correction (AC) maps and estimation of physiological motion. PET listmode data is obtained simultaneously to the MR acquisition which is used for a joint motion estimation and reconstruction of the final MCIR PET. In a first step, dynamic cardiac and respiratory motion resolved 4D MR and PET images are reconstructed. These image series are used in a joint image registration to estimate non-rigid cardiac and respiratory motion fields. In a second step, the motion fields are utilized in a MR MCIR to obtain cardiac and respiratory resolved dynamic MR-based AC maps. In the last step, the non-rigid motion fields and the dynamic AC maps are applied in a PET MCIR to obtain the final motion-corrected PET images. PET-MR data has been obtained in six patients without any known heart disease. Motion amplitudes were between 5.6 and 16 mm, with higher values in the basal compared to the mid-ventricular and apical segments. The proposed joint PET-MR motion estimation provided more accurate motion estimation than using either modality separately. The underestimation of PET uptake due to respiratory and cardiac motion artefacts in the AC maps was up to 17%. The average increase in uptake values using MCIR was 23% ± 10% (p < 0.0001), with values of 28% ± 11% (p < 0.0001) for basal, 21% ± 8% (p < 0.0001) for mid-cavity and 17% ± 7% (p < 0.0001) for apical segments. With the proposed scheme we could ensure high PET image quality and improve local PET uptake quantification by up to 30%. Attenuation correction and motion information was obtained from the same PET-MR raw data, which was obtained during free-breathing to minimize scan times and to increase patient comfort.