Manager Nigel Pearson's son James, Adam Smith and Tom Hopper had their contracts terminated on Wednesday after the team's investigation concluded into the incident on a post-season tour of Thailand.
Leicester, which is owned by Thai business, said it took the strongest possible action to show it is "committed to promoting a positive message of community and family values and equality."
English soccer's anti-racism organization, Kick It Out, said it hopes Leicester's action sets the "decision-making pattern for the future," given that clubs rarely fire players for misconduct.
"Leicester have set the right tone to allow football to assert itself in setting and maintaining the correct standards of conduct to enhance the game's image here and abroad as a source for good," Kick It Out chairman Herman Ouseley said.
"For too long, decision makers at the top of the game have been reluctant to make responsible and authoritative decisions, as employers, to deal effectively and decisively with incidents of serious misconduct and unprofessional behaviour, as well as applying appropriate sanctions."
The video, which was obtained last month by British newspaper The Sunday Mirror, shows the players unclothed and engaging in sex acts. One of them is heard laughingly using a racial slur to describe one of the women.
The story was particularly embarrassing for Leicester because the team is owned by Thai billionaires Vichai and Aiyawatt Srivaddhanaprabha.
The father-and-son tycoons own Thailand's duty-free empire King Power, whose company name is emblazoned on the front of Leicester's team jerseys.
One of the team's main sponsors is the Tourism Authority of Thailand, whose slogan "Amazing Thailand" is prominently displayed throughout the club's stadium, which is called King Power Stadium.
The club was touring Thailand after narrowing avoiding relegation from the Premier League.
None of the fired players have appeared for Leicester in the Premier League. They were loaned out last season in the lower leagues: defender Pearson at Wrexham, goalkeeper Smith at Mansfield and striker Hopper at Scunthorpe. Pearson and Smith are 22 and Hopper is 21.Suggest a correction