Long-range $cis$-regulatory elements such as enhancers coordinate cell-specific transcriptional programmes by engaging in DNA looping interactions with target promoters. Deciphering the interplay between the promoter connectivity and activity of $cis$-regulatory elements during lineage commitment is crucial for understanding developmental transcriptional control. Here, we use Promoter Capture Hi-C to generate a high-resolution atlas of chromosomal interactions involving ~22,000 gene promoters in human pluripotent and lineage-committed cells, identifying putative target genes for known and predicted enhancer elements. We reveal extensive dynamics of $cis$-regulatory contacts upon lineage commitment, including the acquisition and loss of promoter interactions. This spatial rewiring occurs preferentially with predicted changes in the activity of $cis$-regulatory elements and is associated with changes in target gene expression. Our results provide a global and integrated view of promoter interactome dynamics during lineage commitment of human pluripotent cells.