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 species of midge was able to release large volumes of nutrients into the soil, changing the way native species had lived and evolved, a UK team found.
They added the species was well-suited to thrive in the extreme conditions.
Details of the research were presented at the British Ecological Society's annual meeting in Birmingham.
A team from the British Antarctic Survey said the invasive species, the non-biting midge Eretmoptera murphyi, effectively removed one of the brakes on the way that the native community had developed.
"In terms of function, their job is litter turnover - they help things decay in the soil - and the population density of this thing in the area where it has been introduced is responsible for more litter turnover than the community that was already there," explained co-presenter of the research Peter Convey, of the British Antarctic Survey.
"So basically it is bringing a function into an ecosystem that is not very active already. In principle, it can be a fundamental change in the way that ecosystem works."
Speaking to BBC News before the presentation, Prof Convey warned: "If you widen [this issue] beyond this particular species then probably the biggest risk is that we could drive locally or generally extinct some of the unique species that already exist in part of the Antarctic."
He said that in a different project, the team had been looking at the tiny flies' evolution.
"Its native home is sub-Antarctica in South Georgia, and it has been on [the island] for several tens of millions of years.
"South Georgia is its own tectonic plate that has been moving away from South America for 30 or 40 million years.
"The Antarctic peninsula is another tectonic plate of a similar sort, and there are things on there that have got a similar multi-million, if not multi-tens of million-year histories."
But Prof Convey explained that just because the two areas were located in a similar region, it did not mean the transfer of species between them did not have lasting consequences.
"You are looking at almost distinct bio-geographic regions, which have got their own distinct biodiversity.
"So if you transfer things between them - you have things like this fly that is pre-adapted - you also bring potentially new functions into the ecosystem."
The threat of introducing a growing number of invasive species into the Antarctic's long-isolated ecosystems is increasing; the team highlighted that about 5,000 scientific staff and 30,000 tourists were visiting the continent each year.
Prof Convey said: "When people visit the Antarctic - whether that be tourists or people like me - we stop in the sub-Antarctic first, then we go on. So the biggest perceived risk at the moment is that people get a lot of mud on their boots, and then two days later you are in the South Orkney Islands, mud drops off boots - so the things are able to colonise the area.
"And then another day later, the ship reaches Elephant Island, which is at the tip of Antarctic peninsula, and then another day later it has got half-way down the peninsula. So you have got this potential step-carrying of things down the peninsula."
Because species like the midge had the physiological characteristics to survive "all the way down the peninsula", it had the potential to have a wide and lasting impact, he observed.
"If we are not careful about the way we move around then we could be a very good carrying vector."
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.
[NEXT_CONCEPT]
An invasive species has the potential to drastically alter Antarctic ecosystems that have been isolated for millions of years, research suggests.