A native of the Paris region, Yann Genty started handball at the age of 4 as a winger. Eventually converted into a goalkeeper, he stayed 15 years at the Saint-Gratien club before joining Billère where he spent two seasons. He then joined Aurillac and then Istres in 2010, where he replaced Vincent Gérard. In 2014, after two seasons at Cesson, Genty joined Chambéry and was voted best goalkeeper in the Lidl Starligue in his first season. In May 2019, at the age of 37, he was called up for the first time for the France national team.