On 24 July 2017 he reached his highest ATP singles ranking of world No.

Giannessi made his Grand Slam debut at the 2016 US Open as a qualifier where he recorded his first Major win defeating Denis Kudla in five sets.

[1] At the 2021 French Open, he made his debut at this Major after qualifying for the main draw with a win over Francisco Cerundolo.

At the 2022 French Open, although he lost in the third round of qualifying to Sebastian Ofner — he entered the main draw as a lucky loser.

[2] He won his fourth Challenger title and first since 2019 at the 2023 Zadar Open this time with a win over Sebastian Ofner.