The location and movement of mammalian gut tissue progenitors, prior to the expression of tissue-specific genes, has been unknown, but this knowledge is essential to identify transitions that lead to cell type specification. To address this, we used vital dyes to label exposed anterior endoderm cells of early somite stage mouse embryos, cultured the embryos into the tissue bud phase of development, and determined the tissue fate of the dye labeled cells. This approach was performed at three embryonic stages that are prior to, or coincident with, foregut tissue patterning (1-3 somites, 4-6 somites, and 7-10 somites). Short-term labeling experiments tracked the movement of tissue progenitor cells during foregut closure. Surprisingly, we found that two distinct types of endoderm-progenitor cells, lateral and medial, arising from three spatially separated embryonic domains, converge to generate the epithelial cells of the liver bud. Whereas the lateral endoderm-progenitors give rise to descendants that are constrained in tissue fate and position along the anterior-posterior axis of the gut, the medial gut endoderm-progenitors give rise to descendants that stream along the anterior-posterior axis at the ventral midline and contribute to multiple gut tissues. The fate map reveals extensive morphogenetic movement of progenitors prior to tissue specification, it permits a detailed analysis of endoderm tissue patterning, and it illustrates that diverse progenitor domains can give rise to individual tissue cell types.