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
OBJ keeps fueling feud with Josh NormanThe Giants wide receiver had some choice words for the Redskins cornerback.
The Giants BeatYesterday at 12:41 PM
Odell Beckham jabs at Josh Norman yet againThe feud between Odell Beckham Jr. and Josh Norman hasn't exactly been settled just yet.
The Giants BeatThursday at 2:04 PM
Giants 2016 Schedule Preview: RavensThe Giants Beat takes a look at Big Blue's Week 6 opponent, the Baltimore Ravens.
The Giants BeatThursday at 8:31 AM
Giants 2016 Schedule Preview: PackersThe Giants Beat takes a look at Big Blue's Week 5 opponent, the Green Bay Packers.
The Giants BeatWednesday at 8:15 AM