A person familiar with the situation told The Associated Press that Edwards would sign a five-year contract. The person spoke on condition of anonymity because teams can't officially sign free agents until 6 p.m. Friday.
Edwards, who spent the last five seasons with the Minnesota Vikings, fills a major void on the Falcons defensive line. He had 16.5 sacks the past two years and gives Atlanta another pass-rushing threat along with John Abraham.
Earlier Friday, the Falcons cleared $7.8 million in cap room by cutting defensive end Jamal Anderson and receiver Michael Jenkins.