Born at Leuven (Louvain), Geldorp trained in Antwerp, first with Frans Francken and subsequently with Frans Pourbus. He became court painter to Charles of Aragon, Duke of Terranova, whom he accompanied in 1604 to Cologne, where he remained for the rest of his life. Some seventy paintings by him are known, mostly on panel and mostly portraits, including nine in the Rijksmuseum with dates between 1590 and 1610. The majority of his religious and mythological pictures are also of head-and-shoulder length figures. George Geldorp, the portrait painter active in England from 1623 until his death in 1665, was his son.