The Dutch manager, 61, used the N-word in front of his players during the preseason, sources told The Athletic's Jeff Rueter and Sam Stejskal. When confronted about the incident, Jans said he was quoting lyrics from a hip-hop song, Rueter and Stejskal added.
Major League Soccer and FC Cincinnati opened an investigation into the matter, with the club confirming the manager's resignation on Tuesday.
"As Major League Soccer's investigation unfolded and some themes emerged, Ron offered his resignation and we agreed that it was the best course of action for everyone involved with FC Cincinnati," club president Jeff Berding said in a statement.
"We place the utmost importance on a strong culture within our club, beginning in our locker room, and that every person connected with FC Cincinnati feels valued, respected and trusted," Berding added. "Racial and cultural diversity is a major part of what makes the game of soccer so special, and we place the highest priority on respecting every person involved in our game. This includes absolutely everyone associated with our club, from our locker room and front office, all the way through to our fans."
Jans had been with FC Cincinnati since August 2019.
The MLS Players Association (MLSPA) released a scathing statement on the matter later in the day, with executive director Bob Foose saying he's "incredibly disappointed by the attempts to manipulate the public conversation over the last few days with false narratives and strategic leaks to the press ... The narrative that the conduct here involved singing along to song lyrics is completely false, despite the former coach's recent assertions."
He added: "It is our sincere hope that FC Cincinnati will learn from and address these mistakes, and begin to chart a new course forward, one that includes treating all of its players, current and former, with fairness and respect."
The club has now kicked off an "international" search for a new head coach. Yoann Damet will serve as interim boss until a permanent appointment is made.
After missing the playoffs in their inaugural MLS season in 2019, FC Cincinnati will open their sophomore campaign on March 1 against the New York Red Bulls.