Yaakobishvili moved to Barcelona in 2017 after his mother received a job offer in the city, and joined the youth sides of Atlètic Sant Just FC along with his younger brother. In 2021, he was signed by Girona FC, joining their Juvenil squads.
Yaakobishvili made his senior debut with Girona's reserves on 11 December 2022, starting in a 4–1 Tercera Federación home routing of CE L'Hospitalet. He scored his first senior goal the following 12 February, netting the B's second in a 2–0 away win over UE Tona.
Yaakobishvili made his first team debut on 17 January 2024, coming on as a half-time substitute for Juanpe in a 3–1 home win over Rayo Vallecano, for the season's Copa del Rey. On 21 January 2024, he debuted in La Liga in a 5–1 victory over Sevilla FC on the 25 game week of the 2023–24 La Liga season.
On 29 January 2025, Yaakobishvili played his first match in the UEFA Champions League in a 2–1 defeat from Arsenal F.C. on the last match day of the 2024–25 UEFA Champions League league phase. After the match, Michel, the manager of Girona, said that Yaakobishvili is ready for playing in the first team.
On 15 August 2025, Yaakobishvili was loaned to Segunda División side FC Andorra for one year; he became the third loanee of Girona to the club, and also joined his brother Áron in the squad. The following 22 January, after being rarely used, he moved to Primera Federación side CD Tenerife on loan until June.
On 27 August 2026, Yaakobishvili was loaned to Atlético Madrileño also in division three, for one year.