The 25-year-old has been a regular fixture in the Forest squad since completing a £12.7m deal from Stuttgart in the summer of 2022.
Mangala has started 19 of his 20 Premier League appearances this term, including the last two league matches against Brentford and Arsenal.
However, Forest have allowed the Belgium international to join French club Lyon on loan for the remainder of the 2023-24 season.
Forest have agreed a deal which includes a £10m loan fee plus £3m in add-ons, while there is an option for Lyon to purchase Mangala for £20m.
Should the Ligue 1 club exercise their right to recruit the Belgian on a permanent basis, Forest will be entitled to a 10% sell-on from any future sale.
Mangala joins a side that a currently fighting for the retain their Ligue 1 status, with Lyon currently sitting in the relegation playoff spot on goal difference.
While Mangala has left the club, Nuno Espirito Santos has strengthened his squad on deadline day with the addition of Belgian goalkeeper Matz Sels.