Born in Santiago de Cuba on 12 July 1983, she started her sports career in track and field athletics. In 2006 she married an Italian man and relocated to Casalpalocco, a borough in Rome. She acquired Italian citizenship in 2008. She broke the Italian record at 400 meters with a time of 50.83 seconds. This performance took place in Beijing during the semi-final of the 400 meters. Despite this effort Grenot did not reach the final. In 2009 she won a gold medal for the 400 meters at the XVI Mediterranean Games with a time of 50.30 seconds, a new Italian record.
In 2014, she was first in the 400 meters at the European Championships, becoming the first Italian woman to win an international track title since 1938.