Fox News has agreed to pay $12 million to Abby Grossberg, a former Fox News producer who had accused the network of operating a hostile and discriminatory workplace and of coercing her into providing false testimony in a deposition.

Parisis G. Filippatos, a lawyer for Ms. Grossberg, said that the settlement concluded all of Ms. Grossberg’s claims against Fox and the people she had named in her complaints, which included the former host Tucker Carlson and some of his producers.