He served as apprentice to Joseph Collyer the younger, and subsequently became assistant to James Heath.
He became better known to the public by his engravings from the pictures and drawings of Richard Cook, R.A., and some of these were considered among the finest specimens of book illustrations then produced in England.
Engleheart engraved nearly thirty of Smirke's designs for their edition of Don Quixote.
His services were enlisted by Sir David Wilkie, R.A., to engrave his Duncan Gray and The only Daughter, which are the works by which Engleheart is chiefly known.
His last important work was an engraving from the picture by William Hilton, R.A., of Serena rescued by Sir Calepine, the Red Cross Knight.