The 23-year-old is due to undergo his medical at Strasbourg on Monday before signing a five-year contract, with L'Équipe reporting a fee of around €3m, and Gladbach also said to have secured a 10% sell-on clause.
Reyna had joined Borussia Monchengladbach a year ago from Borussia Dortmund for a fee in the region of €4m but never settled, hampered by injury problems throughout his spell with the Fohlen. He made just 20 appearances in all competitions, managing only one goal and one assist, starting only four Bundesliga matches all season.
After 125 Bundesliga appearances across his career, the right-footed attacker now leaves Germany behind for good after seven years in the country, most of them spent at Dortmund, for whom he made 147 appearances, scoring 19 goals and adding 18 assists, and helped win the 2021 DFB-Pokal, before an underwhelming Nottingham Forest loan spell during the 2023-24 season also failed to reignite his career.
Reyna, capped 43 times by the United States, represented his country at this summer's World Cup, scoring once in five appearances, before returning to a Gladbach side that never found a settled role for him, with academy product Wael Mohya and Austrian playmaker Kevin Stöger both moving ahead of him in the pecking order over the course of the season.
Recurring physical issues repeatedly interrupted his progress, even after an opportunity appeared to open up on the left of Gladbach's attack following Robin Hack's meniscus surgery earlier in the campaign.
At Strasbourg, Reyna will move into a French top-flight side building around a new generation of attacking talent, and is expected to compete with Paraguay international Julio Enciso for a role behind the front line, arriving as a replacement of sorts for Valentin Barco, who left the Alsace club this summer.