Police were called to Junction 3 near Chatham at about 3.30am on Tuesday, May 17, to a report of concern for the welfare of a man. Officers found a body at the scene and closed the road.
Kent Police said in a statement: “The death is not being treated as suspicious and police are compiling a report for the coroner.
“The man’s family have been informed.”
Both carriageways have remained closed to traffic with vehicles being directed to leave at Junction 3 before re-joining the carriageway.
Motorists have been advised to consider alternative routes to avoid congestion.
Drivers stuck in traffic jams have been warned of delays of up to 90 minutes.
National Highways said in a statement: “The incident which occurred shortly before 4am this morning is being led by Kent Police.
“National Highways traffic officers and service providers are assisting police with traffic management.
“Traffic is being diverted via the exit and entry slip roads of J3. This is known as an ‘up and over’ closure.
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It advised drivers to allow an extra 30 minutes on to journey times.
Meanwhile, the M5 motorway southbound near Gloucestershire has reopened after the death of a woman in a crash involving two vans and a lorry.
The fatal collision between junction 5 for Wychbold and 6 for Worcester happened at about 1.30pm on Monday, May 16.
West Midlands Ambulance Service was called at 1.26pm with the Midlands Air Ambulance sent to the scene.
An ambulance service spokeswoman said: “Crews arrived at the scene to find the driver of the car in a critical condition after coming into collision with an HGV.
“Crews worked quickly to administer advanced trauma care to the woman. But sadly, despite their best efforts, nothing could be done to save her, and she was confirmed deceased on scene.”