Bryant told ESPNDallas.com Friday afternoon that he was diagnosed with the condition at the National Scouting Combine in March.
"The teams that I visited said I was fine," Bryant said. "I feel fine. They worked me out and said I was fine."
A normal heart rate is 50 to 100 beats per minute, but irregular heartbeats -- or arrhythmias -- don't occur together, according to the health website WebMD. In the United States, more than 850,000 people are hospitalized for an irregular heartbeat each year.
"All of our doctors reviewed that, and it's just not something we were concerned about," Cowboys owner and general manager Jerry Jones told ESPN Dallas.
Friday night, Jones told reporters he was diagnosed with an irregular heartbeat after he purchased the team in 1989. He noticed when he was talking to people he was experiencing a shortness of breath.
"At least 30 percent of this country has what I have," Jones said regarding an irregular heartbeat. "My point is, there is nothing about Dez Bryant that caused us to in any way look differently at him about his ability to have a football career in the NFL or his ability to have a normal life."
Bryant said he was surprised he was told he had the condition.
The only real injury he's had in the last few weeks was a hamstring pull that caused him to miss working out at the combine, which also bothered him at his private pro day for college scouts.
"It kind of surprised me, but it's Ok, but I'm fine," Bryant said. "I've been training and working out on my own."