Reece, 28, joined the Crusaders in 2019 after making his first-class debut for Waikato, and marked his debut in Super Rugby with a two-try man of the match performance against the Chiefs.
He went on to share the Crusaders' successes in Super Rugby Aotearoa in 2020, 2021, and 2022, and in Super Rugby Pacific in 2023 and 2025.
During the 2025 season, he became Super Rugby's highest try scorer with 66 tries.
French sports outlet L'Equipe said Reece has signed a three-year contract with Perpignan, the bottom-ranked team in the Top 14 competition.
He debuted for the All Blacks in 2019 and has scored 22 Test tries.
Reece said, "The club has given me everything, and I will forever be grateful for all the opportunities I have had in the red and black. I'll miss so many things, but mainly the people – they are what make the Crusaders so special.
"It's a bittersweet time, and this hasn't been an easy decision at all, but my family and I are excited for this next adventure in France.
"However, I still have a job to do here. I can't wait for this season. I'm hoping I can finish on a high and win one last title, and to do that under the roof at the new stadium will be unreal."
Crusaders coach Rob Penney said Reece had made a significant impact on the southern region.
"The amount of growth Sevu has had in his time in the red and black since 2019 is a credit to his character.
"While at this club, he's started his family, achieved a huge amount of milestones, and helped lead this team to six titles. He's also on track to earn his 100th Crusaders' cap [he's on 88] this year which will be a special way to end his last season with us."