It had been reported that he would continue to be an executive producer of the show he helped create.
He tweeted on Saturday that he would "devote zero time" to the new series, which will be hosted by actor and politician Arnold Schwarzenegger.
However, Mr Trump did reaffirm that he has a "big stake" in the show.
Mr Trump fronted the series, which is owned by MGM and aired by NBC, until 2015, when his political career took over.