Police were called to the slip road at the junction with the A293, and the road was closed until 10am.
The man who fell has not yet been identified, but was sadly pronounced dead at the scene, police said.
Enquiries are ongoing to establish the full circumstances and police are appealing for witnesses – or anyone with dash cam footage – to report it online or call 101, quoting Operation Flexor.
The #A27 has RE-OPENED westbound between the #A2038 near #Portslade and #A293 near #Shoreham-by-sea after the earlier incident. Delays remain on approach, which should now begin to ease. Thank you for your patience. pic.twitter.com/TGalQsyJvR
The incident is reported to have occurred about 6.50am on Friday, approximately one mile east of Southwick tunnel.
The A27 westbound is currently closed after the incident at about 6.40am, approximately one mile east of the Southwick tunnel, Sussex Police said.
A spokesperson for Sussex Police said: The A27 westbound is currently closed at Hangleton following a report of a man having fallen from a bridge.
Motorists are advised to seek alternative routes for the time being; the eastbound carriageway remains open.
Sussex Traffic Watch said at 8am: A27 westbound remains closed between the Dyke Road junction and Hangleton due to an ongoing police incident queuing traffic from Hollingbury. Local diversion routes also very congested.