The 22-year-old was told to find a new club after failing to establish himself as a first team regular at Borussia Dortmund.
Reyna spent 2023-24 on loan at Premier League side Nottingham Forest before going on to score two goals and provide one assist in his 26 games for Dortmund last season.
He has now signed a three-year contract at Bundesliga rivals Borussia Mönchengladbach for a reported fee of €7 million with add-ons and includes a 15 percent sell-on clause.
“Borussia are a fantastic, big club," said Reyna to the team's official website. "I’m delighted that the transfer has been able to be completed and am looking forward to getting to know everyone here, as well as tackling the upcoming games together.”
