West Yorkshire Police shut the trans-Pennine motorway for several hours on Sunday morning following the fatal fall from the Scammonden Bridge near Huddersfield.
Officers only initially referred to an "ongoing police incident".
The force later said a driver had seen a man fall at around 8.40am, leading to the full closure of the motorway as the emergency services attended.
Inspector Graham Hawcroft said: "He had fallen onto the verge next to the carriageway.
"Officers attended and located him and he was declared dead at the scene.
"His death is not being treated as suspicious and his next of kin have been informed.
"The motorway was re-opened at 11.55am."