Lineage conversion of one somatic cell type to another is an attractive approach for generating specific human cell types. Lineage conversion can be direct, in the absence of proliferation and multipotent progenitor generation, or indirect, by the generation of expandable multipotent progenitor states. We report the development of a reprogramming methodology in which cells transition through a plastic intermediate state, induced by brief exposure to reprogramming factors, followed by differentiation. We use this approach to convert human fibroblasts to mesodermal progenitor cells, including by non-integrative approaches. These progenitor cells demonstrated bipotent differentiation potential and could generate endothelial and smooth muscle lineages. Differentiated endothelial cells exhibited neo-angiogenesis and anastomosis in vivo. This methodology for indirect lineage conversion to angioblast-like cells adds to the armamentarium of reprogramming approaches aimed at the study and treatment of ischemic pathologies.