Hendrick Motorsports notes 44-year-old Johnson "never experienced symptoms".
After Johnson initially tested positive, four Hendrick crew members were tested for COVID-19, and they all had negative results, the team said.
Dover International Speedway will host only one NASCAR Cup Series race weekend next year and beyond.
Johnson will drive his No. 48 Chevrolet in Sunday's Cup race at Kentucky Speedway.
Missing the Brickyard 400 dropped Johnson to 15th in the driver standings, 46 points above the cutoff for playoffs. NASCAR confirmed Wednesday that Johnson has been cleared to return.
As announced in late June, New York is requiring anyone visiting from a state where coronavirus rates are high to quarantine for 14 days.
NASCAR will return to Daytona two weeks later as scheduled for the regular-season finale on the oval.
Speedway officials continue to work with local, state and federal health officials, as well as Delaware Gov. John Carney, on whether fans will be allowed in the stands with appropriate social distancing for the August events.
No spectators will be in attendance for this Sunday's race in Kentucky, the 13th Cup race since NASCAR resumed racing eight weeks ago. "The sport of NASCAR gets to add a surprise chapter of road course racing to the venue's legacy". The Saturday, Aug. 22 Xfinity Series race will start at 12:30 p.m. (NBCSN) while the Sunday, Aug. 23 event will begin at 1 p.m. (NBCSN).
Additionally, Truck races originally scheduled to run at Eldora Speedway and Canadian Tire Motorsports Park were realigned to a track and date yet to be announced; the series will not race at either of those tracks in 2020.
Friday: NASCAR Xfinity Series Alsco 300, 8 p.m. "We are certainly looking forward to a historic weekend here in Dover", said Mike Tatoian, Dover International Speedway's CEO.