Resting-state fMRI is commonly used to derive brain parcellations, which are widely used for dimensionality reduction and interpreting human neuroscience studies. We previously developed a model that integrates local and global approaches for estimating areal-level cortical parcellations. The resulting local-global parcellations are often referred to as the Schaefer parcellations. However, the lack of homotopic correspondence between left and right Schaefer parcels has limited their use for brain lateralization studies. Here, we extend our previous model to derive homotopic areal-level parcellations. Using resting-fMRI and task-fMRI across diverse scanners, acquisition protocols, preprocessing and demographics, we show that the resulting homotopic parcellations are as homogeneous as the Schaefer parcellations, while being more homogeneous than five publicly available parcellations. Furthermore, weaker correlations between homotopic parcels are associated with greater lateralization in resting network organization, as well as lateralization in language and motor task activation. Finally, the homotopic parcellations agree with the boundaries of a number of cortical areas estimated from histology and visuotopic fMRI, while capturing sub-areal (e.g., somatotopic and visuotopic) features. Overall, these results suggest that the homotopic local-global parcellations represent neurobiologically meaningful subdivisions of the human cerebral cortex and will be a useful resource for future studies. Multi-resolution parcellations estimated from 1479 participants are publicly available (https://github.com/ThomasYeoLab/CBIG/tree/master/stable_projects/brain_parcellation/Yan2023_homotopic).