Ryan had one year left on his current three-year deal.
Dallas, which was eliminated from playoff contention during the final week of the regular season, finished 19th in the NFL in total defense this year.
Cowboys owner/general manager Jerry Jones had hinted in previous weeks "changes" would be coming.
Thus far, this is the first ax to drop.
More to come on this breaking story.
Rob Ryan fired
The Giants Beat Top Stories
Giants sign veteran RB Shaun DraughnThe journeyman running back is excited to be back in the playoff hunt.
The Giants Beat11:20 AM
Scouting the NFL Draft: Leonard FournetteThe Giants have a hole at running back, but should they kick the tires are one of the top RB prospects of the 2017 draft class?
The Giants BeatMonday at 2:20 PM
The Giants Beat Podcast: NFL Draft PreviewThe Giants Beat's dynamic duo discusses this month's NFL draft prospects that Big Blue should keep an eye on and recaps the team's free agent signings.
The Giants BeatMonday at 11:05 AM
Scouting the Draft: Cam RobinsonScout takes a look at the offensive tackle out of Alabama and how he can help fortify Big Blue's offensive line.
The Giants BeatSaturday at 4:59 PM