Ex-NFL Coach Rex Ryan's Alleged Hit-And-Run Caught On Camera

Rex Ryan was arrested this week for an alleged hit-and-run ... and he was captured thanks to the two quick-thinking people he allegedly hit ... TMZ has learned.

According to a warrant, obtained by TMZ ... last week, the ex-NFL coach jumped out of his pickup truck at an intersection in Nashville, Tennessee, and he got into a heated argument with two pedestrians after he allegedly ran over their feet.

Cops said Ryan then hopped back into his vehicle and took off ... but not before the alleged victims snapped photos of his license plate with the cameras on their phones.

Police say Ryan gave his name to the alleged victims, who also got a good look at Ryan's face, making it easy to ID him with a quick Google search.

According to the warrant, the police matched the vehicle tag, the registered owner's information, and the license plate number provided by the alleged victims to Ryan.

The Nashville-Metropolitan PD says Ryan surrendered to authorities Wednesday after he allegedly ran over the feet of the two pedestrians who were crossing the street just before midnight last Thursday.

Cops say the wheels of Ryan's pickup truck left black scuff marks on the shoes of the pedestrians. They noted that one alleged victim -- a female -- was also struck in the leg by the vehicle and suffered a scratch.