In a letter to President Barack Obama, Bryson said he is concerned his seizure "could be a distraction" from his performance as secretary.
The president has accepted Bryson's resignation. Mr. Obama thanked Bryson for what he called the "invaluable experience and expertise" he brought to the administration.
Bryson, 68, had been on medical leave since last week. White House officials said Bryson suffered a seizure on June 9 when he crashed his Lexus into two cars in the San Gabriel Valley.
Police said Bryson was driving alone when he hit a vehicle that was stopped for a passing train. Nobody was injured. As Bryson departed, investigators said he hit the car again. He then hit a second car nearby and was found unconscious in his car. According to police, Bryson took a breathalyzer test that didn't detect any alcohol.
San Gabriel police said they are waiting for Bryson's medical records, and they have asked for toxicology tests before deciding whether charges will be filed.
When he went on leave, Bryson transferred his duties to Deputy Commerce Secretary Rebecca Blank. Until the White House names a replacement for Bryson, Blank will continue as acting commerce secretary.
The Associated Press contributed to this report.