Lynn made the announcement to players during a Zoom meeting shown in the opening minutes of HBO's "Hard Knocks" series which debuted its latest season Tuesday night.
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"I can't promise you're not going to get infected," Lynn tells his players.
"I got infected."
The camera shows the reaction of several players, who are apparently hearing the news for the first time.
Lynn, 51, did not reveal when he was tested or whether he is still considered to be positive for the virus. He also did not disclose any symptoms, though he appeared healthy in the video.
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Lynn is the third NFL head coach to disclose a positive test for COVID-19, including Sean Payton of the New Orleans Saints and Doug Pederson of the Philadelphia Eagles.
Lynn is entering his fourth season with the team and has compiled a 26-22 record.
The team has not released any statements about Lynn's announcement.