The 26-year-old back-row forward has made 16 appearances since joining Edinburgh from Fiji Sevens in 2019 and made his Test debut in 2020.
He set up two tries during Edinburgh's 66-3 Challenge Cup win against Brive on Friday after two months out with a knee injury sustained during last November’s Autumn International against Spain.
Kunavula, who joins fellow Fijian star Viliame Mata in committing his long-term future to the club, said: "Firstly, I want to thank the Lord God for giving me strength and power and I want to thank all of the staff and coaches for giving me a chance and a new opportunity with a new deal. I really appreciate it and I’m really happy.
"Edinburgh feels like home, it means a lot to me. I've never signed for another club, so I appreciate it here.
"I enjoyed being back on the field after being away injured, which was tough for me, but I was really happy to be given another chance against Brive.
"I'm looking forward now. I'm happy because I'm getting a lot of opportunities to play. Next year is a World Cup year, so I'm going to work hard to improve myself and I want to try hard to play as much as I can."
Kunavula was voted Edinburgh's most improved player last season and scored a try against the All Blacks during the summer internationals.
He was part of a Fiji Sevens side that claimed silver at the 2018 Commonwealth Games and made his Fijian Test debut against Georgia at BT Murrayfield in 2020.
Head coach Mike Blair added: "It's brilliant that we're able to re-sign Mesu. He's a player with a hugely exciting skillset and a guy that is really popular at the club.
"His physical threat is obvious but he also has great awareness of the space around him. He uses his offloading game to exploit that space, which was evident in Friday night's win over Brive. I thought he had an exceptional game.
"It's great that Mesu feels like Edinburgh is home and we're really excited to see him continue to develop among a talented back-row group."