In a joint statement, a Fox News spokeswoman and Douglas H. Wigdor, a lawyer for the employees involved, said, “The parties have reached mutual agreements that resolve various cases involving former Fox News employees.”

Mr. Wright informed Fox News on Tuesday of his “desire to pursue new opportunities,” the network and Mr. Wigdor said in statements. In the statements, the network thanked Mr. Wright “for his contributions over the years”; and Mr. Wright thanked Fox News and “wishes it well as he moves forward to the next phase of his career.”

The agreement represents a push by Fox News and 21st Century Fox to move past the negative attention drawn by scandals — including sexual harassment claims — that led to sweeping changes at the top of the network: the ousting of the network’s founding chairman, Roger Ailes; Bill O’Reilly, the top-rated host on cable news; and several other employees. The controversy also prompted a criminal investigation into Fox News’s handling of sexual harassment complaints.

The drama burst into public view in July 2016, when the former anchor Gretchen Carlson sued Mr. Ailes for sexual harassment. After Mr. Ailes was forced out of the network and Ms. Carlson received a $20 million settlement, several other employees came forward with sexual harassment and gender and racial discrimination claims. Some disputes were settled confidentially, while others became public lawsuits, leading to a steady drumbeat of negative headlines and mounting legal costs. By the end of last June, 21st Century Fox had incurred about $50 million in costs in the previous year that were tied to the settlement of sexual harassment and discrimination allegations at Fox News.

Several of the lawsuits were handled by Mr. Wigdor, a self-described conservative Republican who has said that he was at war with Fox News. Mr. Wigdor has been a vocal critic of what he described as a systemic culture of discrimination at Fox News, frequently speaking to the media and even testifying before the British regulators reviewing 21st Century Fox’s $15 billion bid for Sky, the European satellite giant. (Mr. Wigdor’s firm also represented clients in a racial discrimination suit against The New York Times.)