Luka Gugeshashvili was born on September 29, 1999 in Tbilisi, Georgia, and began his career in the Dinamo Tbilisi youth system.

The Georgian shot stopper attracted the interest of Polish club Jagiellonia Bialystok, who signed him in 2016. In order to gain more experience, he was loaned out to lower-division teams.

In the 2017–18 season, he played for Podlasie, where he made 16 appearances. The following season, he moved to Dila Gori in Georgia, where he made 35 appearances, keeping 15 clean sheets, and establishing himself as a first-team regular.

In 2019, he tried his luck in Spain, with Granada’s second team, where he recorded 5 appearances. He returned to Dila Gori in the 2020–21 for a two-year period, where he made 54 appearances with 19 clean sheets and established himself as one of the top young goalkeepers in his country.

In 2022, Qarabag from Azerbaijan acquired him initially on loan, before completing his transfer and becoming a permanent member of the team. He played for Qarabag for three seasons and recorded a total of 44 appearances with 19 clean sheets, also competing in European competitions. During his tenure in Azerbaijan, he won three championships and two cups.

In January 2024, he moved to Greece with Panserraikos, where he has made 25 appearances to date, impressing with his performances.

At international level, Gugeshashvili has played for all of Georgia’s youth teams and is now a member of the men’s national team, having made two appearances so far.