He was born to a family of gem-makers in Rome, where he became a pupil of Benedetto Luti and painted mainly historical and devotional subjects. He painted a St. Camillus in Santa Maria Maddalena, in which he has aspired to the imitation of Domenichino. His Resuscitation of Tabitha in Santa Maria degli Angeli e dei Martiri replicates a mosaic in St. Peter's Basilica. He also painted in fresco the ceilings of the tribunes in Santa Maria in Vallicella and San Gregorio, and was much employed in painting figures in the landscapes of other artists, particularly in those of Jan Frans van Bloemen (Orizonte). Costanzi also traveled to France and Spain.
Costanzi painted a portrait of George Keith, Earl Mareschal of Scotland, in Rome in 1752, now in the National Portrait Gallery, and St. Pancras & Infant Christ, now in the Dublin National Gallery.
- Bryan, Michael (1886). In Robert Edmund Graves. Dictionary of Painters and Engravers, Biographical and Critical (Volume I: A-K). York St. #4, Covent Garden, London; Original from Fogg Library, Digitized May 18, 2007: George Bell and Sons. pp. page 316.
- Getty biography and Getty database record