The astrophysicist Neil deGrasse Tyson will return to television after the broadcasters of his shows announced Friday that they had completed their investigation into sexual misconduct allegations against him.

“The investigation is complete, and we are moving forward with both ‘StarTalk’ and ‘Cosmos,’” Fox Broadcasting and National Geographic said of his two shows. “‘StarTalk’ will return to the air with the remaining 13 episodes in April on National Geographic, and both Fox and National Geographic are committed to finding an air date for ‘Cosmos.’ There will be no further comment.”

The statement did not say what investigators concluded about the complaints. Dr. Tyson was accused in December of behaving inappropriately with two women, in an article published by the website Patheos.

One accusation came from Ashley Watson, his assistant on “Cosmos,” who said that during a visit to his apartment, which she took to be a work visit, he made her feel uncomfortable by holding her hands and looking into her eyes in what he called a Native American handshake. As she was leaving, she said, he told her, “I want you to know that I want to hug you so bad right now, but I know that if I do I’ll just want more.” She quit the show.