PET is an established modality for myocardial perfusion imaging (MPI) which enables quantification of absolute myocardial blood flow (MBF) using dynamic imaging and kinetic modeling. However, heart motion and partial volume effects (PVE) significantly limit the spatial resolution and quantitative accuracy of PET MPI. Simultaneous PET-MR offers a solution to the motion problem in PET by enabling MR-based motion correction of PET data. The aim of this study was to develop a motion and PVE correction methodology for PET MPI using simultaneous PET-MR, and to assess its impact on both static and dynamic PET MPI using 18F-Flurpiridaz, a novel 18F-labeled perfusion tracer. Two dynamic 18F-Flurpiridaz MPI scans were performed on healthy pigs using a PET-MR scanner. Cardiac motion was tracked using a dedicated tagged-MRI (tMR) sequence. Motion fields were estimated using non-rigid registration of tMR images and used to calculate motion-dependent attenuation maps. Motion correction of PET data was achieved by incorporating tMR-based motion fields and motion-dependent attenuation coefficients into image reconstruction. Dynamic and static PET datasets were created for each scan. Each dataset was reconstructed as (i) Ungated, (ii) Gated (end-diastolic phase), and (iii) Motion-Corrected (MoCo), each without and with point spread function (PSF) modeling for PVE correction. Myocardium-to-blood concentration ratios (MBR) and apparent wall thickness were calculated to assess image quality for static MPI. For dynamic MPI, segment- and voxel-wise MBF values were estimated by non-linear fitting of a 2-tissue compartment model to tissue time-activity-curves. MoCo and Gating respectively decreased mean apparent wall thickness by 15.1% and 14.4% and increased MBR by 20.3% and 13.6% compared to Ungated images (P < 0.01). Combined motion and PSF correction (MoCo-PSF) yielded 30.9% (15.7%) lower wall thickness and 82.2% (20.5%) higher MBR compared to Ungated data reconstructed without (with) PSF modeling (P < 0.01). For dynamic PET, mean MBF across all segments were comparable for MoCo (0.72 ± 0.21 ml/min/ml) and Gating (0.69 ± 0.18 ml/min/ml). Ungated data yielded significantly lower mean MBF (0.59 ± 0.16 ml/min/ml). Mean MBF for MoCo-PSF was 0.80 ± 0.22 ml/min/ml, which was 37.9% (25.0%) higher than that obtained from Ungated data without (with) PSF correction (P < 0.01). The developed methodology holds promise to improve the image quality and sensitivity of PET MPI studies performed using PET-MR.