Music at the three-day festival, on Bramham Park, finished on Sunday night, but the campsite remained open until 12pm today.
Thousands of people packed up their tents and left the festival site this morning, causing queuing traffic around the site.
Traffic is extremely heavy on the A1M Northbound between Junction 43 and Junction 46.
Highways England estimate delays of around 40 minutes.
Cars driving into the festival to pick up friends or family have also been blamed for the tailbacks, as well as people travelling to the Yorkshire Coast.
At 12.30pm, Highways England tweeted: "Current delays of approximately 40 minutes on the A1M northbound and southbound prior to J44 Leeds (A64) due to traffic heading for Leeds Festival and the Yorkshire Coast.
"Please allow extra time for your journey as times may increase further."
The West Yorkshire Roads Policing Unit has also urged drivers to take care on the A1M due to the large volume of people leaving Leeds Festival.
They warned to plan extra time for journeys and concentrate carefully, as traffic may suddenly slow or stop.