The fix will include hardware and software upgrades, including replacing an emissions catalyst but will reduce vehicle fuel economy ratings by as much as 2 miles per gallon.
The world's largest automaker will still need to obtain approval for a resale plan for the 2009-2014 model diesel vehicles after making repairs - something that is expected in the coming weeks - but the fix is a significant milestone for the company that aims to move beyond its diesel emissions crisis.
Volkswagen said in a statement it was pleased with the approval and that it means 98 percent of 2.0-liter diesel vehicles have been approved for a fix. Regulators said extensive testing shows the fix will not affect "vehicle reliability or durability."
In March, Volkswagen pleaded guilty to three felonies in a U.S. court and admitted it used secret software that allowed vehicles to emit pollution at up to 40 times the legal limit.
The September 2015 disclosure that VW intentionally cheated on emissions tests for at least six years led to the ouster of its chief executive, damaged the company's reputation around the world and prompted massive bills.
Volkswagen agreed last year to offer to buy back up to 475,000 diesel vehicles with 2.0-liter engines that had been sold in the United States, including the vehicles that won approval on Thursday for a fix. Thursday's approval means that the automaker can now offer hardware and software upgrades and compensation to owners.
The approval is also a key step toward allowing the carmaker to resell or potentially export tens of thousands of diesel cars it has repurchased and is storing all over the United States.
As of the end of May, Volkswagen had 37 secure storage facilities around the United States housing close to 275,000 vehicles. Those places include a shuttered suburban Detroit football stadium, a former Minnesota paper mill and a field near a raceway in Colorado.
The automaker has spent more than $6.3 billion to repurchase 2.0-liter vehicles and compensate owners.
The vehicles winning approval for an upgrade are the oldest of the models that came under scrutiny in the company's diesel cheating scandal. Those models are known as "Generation One."
Earlier this year, EPA approved fixes for two newer generations of diesel cars - including 84,000 Passat diesel vehicles of model years 2012-2014 with automatic transmissions in "Generation Two" and 67,000 model 2015 diesels in "Generation 3." The only vehicles without a fix are manual 2012-2014 Passat diesels.
Volkswagen has agreed to spend up to $25 billion to address claims from U.S. owners, environmental regulators, states and dealers, and offered to buy back about 500,000 polluting U.S. vehicles, including some larger 3.0 liter vehicles.
Reporting by David Shepardson