Trevor Campbell, 59, from Sompting, was treated by paramedics but died at the scene.
He was struck at about 06:00 GMT on the eastbound carriageway in Lancing.
A 58-year-old man from Climping had been arrested on suspicion of causing death by careless driving.
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Mr Campbell, his wife Rosemary said the family was devastated.
She said he left a daughter, Ella, 28, and a granddaughter, Aerith, aged two.
"Trevor absolutely doted on Aerith, just as he did our own daughter, and his death is going to leave a huge gap in our family," she said.
Mr Campbell, a porter at Lancing College, was taking his usual walk to work when he was killed, police said.
Lancing College headmaster Dominic Oliver said he was a long-serving and loyal member of the team, and the Lancing community was saddened and shocked by his death.
A man arrested over the death of a pedestrian hit by a car on the A27 in West Sussex on Thursday has been released without charge.