Suk scored six goals in 26 Ligue 1 appearances for Troyes on loan from Porto last season, but couldn't prevent the team from suffering relegation from the top flight.
He signed a permanent deal with Troyes in June and played their first second-tier game of the season, before abruptly departing.
"The decision is the result of unprofessional acts by the player, who was under contract until June 30, 2021," said Troyes in a statement.
"But we cannot, with the project we're trying to put in place, retain individuals who don't feel concerned by that."
The 27-year-old former Ajax youth-team player, who missed out on a place in the Korean World Cup squad despite playing twice in qualifying, has joined Reims on a four-year deal.
"Suk shone in the first division in the Netherlands, Portugal and last season in Ligue 1," said Reims president Jean-Pierre Caillot.
"He is a powerful player who can serve as a focal point in attack and who has undeniable qualities as a finisher."
Reims were promoted last season as Ligue 2 champions.