Marine bioinvasions are potential threats to biodiversity and ecosystems services, being one of the major environmental, human health and socio-economic problems throughout the world. In 2005, a sponge species never reported before to the Atlantic Ocean was detected in Rio de Janeiro (Brazil). This species was initially considered new to science and in less than a decade its populations became very abundant and widespread in the Brazilian coast. In the present work, we performed detailed morphological and molecular analyses of this supposedly new species and found out that it is in fact the Indo-Pacific calcareous sponge Heteropia glomerosa (Bowerbank, 1873). Heteropia glomerosa is the third alien species of calcareous sponge reported in the Atlantic and the second one that allegedly came from the Indo-Pacific. To confirm the taxonomic identification of the Atlantic specimens, we used morphological and molecular tools and re-described the holotypes of H. glomerosa and Uteopsis argentea (Poléjaeff, 1883). We discuss the possibility that biofouling is the introduction source for sponges and present the known distribution of H. glomerosa. Moreover, we verified that H. glomerosa fits seven out of 10 criteria proposed for recognizing alien species. Although this species can be recognized as introduced in the Atlantic Ocean, studies on population genetics, phylogeography, reproduction strategies, larval behaviour, and ecology will be necessary to allow a better evaluation of its invasive potential.