Thousands of drivers spent days in queues to reach the Port of Dover and Eurotunnel after France temporarily closed its border on 20 December.
The move came after the discovery of a fast-spreading Covid-19 variant in the UK, with French authorities easing restrictions on Wednesday.
Around 3,000 hauliers were waiting to cross into France from Kent on the evening of Christmas Day.
But on Sunday, DfT said there were only 180 heavy goods vehicles on the M20 waiting for the Eurotunnel.
The department also said there were fewer than 15 lorries at Manston Airport, where drivers would be tested before heading to the Port of Dover.
DfT has asked heavy goods vehicle drivers to avoid Kent, as road haulage groups say those who held off leaving for the border over the festive period are likely to join the queue soon.
Drivers wishing to enter France from Britain must now show proof of a negative Covid-19 test taken in the previous 72 hours.
As of Sunday, a total of 17,988 Covid-19 tests had been completed, DfT said.
Transport Secretary Grant Shapps previously said there had been 36 positive results out of the 15,000 drivers who had been tested for coronavirus by midday on Boxing Day.
On Sunday, Transport Minister Robert Courts expressed his thanks to those at the Port of Dover, Eurotunnel, ferry companies P&O and DFDS, as well as volunteers who had provided food and water to the drivers.
Mr Courts said: "Hundreds of hard-working, diligent staff from the back office to the captains who've come together over this festive period, they've given up their Christmas days to help ensure that hauliers and passengers can get on their way as quickly as possible.
"I have been immensely impressed by all of your efforts. We've seen the very best of Britain illustrated during this time. The Port of Dover, staying open throughout Christmas Day and overnight, P&O running services throughout the night and DFDS operating on Christmas Day."
Mr Courts added: "There's still more to do but with progress made on clearing the Manston site and work on getting hauliers holding in Operations Brock and Stack moving, there is light at the end of the tunnel."
Volunteers - including individuals from nearby communities, the Salvation Army, Muslim group Al-Khair Foundation, HM Coastguard and Kent County Council - have been delivering thousands of warm meals and water to the drivers.
The Road Haulage Association (RHA) has co-ordinated with businesses providing food and water to the drivers over the festive period.
Tesco provided 600 food parcels, 24 pallets of staples and thousands of sausage rolls, distributed on Christmas Eve and Christmas Day.
And on Sunday, Eddie Stobart Logistics delivered thousands of food items to the stuck hauliers.
RHA chief executive Richard Burnett said: "Although nothing can compare to spending Christmas with the family, these drivers have been denied that through no fault of their own.
"Providing them with food is the least that we can do. This is a great seasonal example of the industry pulling together to support its own driver community."
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