The 35-year-old man, who has not been named, was walking on Coopers Green Road in Uckfield at about 01:00 GMT on Saturday.
A vehicle believed to have been involved was later traced by police to a nearby address.
A 26-year-old man was subsequently arrested on suspicion of causing death by dangerous driving. He has been released on bail until 28 February.

"I've been sitting on these banks for the last 25 years and this is the most bodies I've ever seen," says 53-year-old Krishna Ghimire, one of the temple's many priests.
Pashputinath, which spans the banks of the Bagmati River, is the most revered Hindu temple in Nepal.
This is where the dead are cremated - on ghats (cremation grounds) that jut out over the muddy water.
Earthquake victims arrive here a dozen each hour. On Sunday, there were nearly 200 cremations. More than 100 are expected on Tuesday.
"Yesterday was so depressing," says the priest.
"Nearly 20 bodies arrived in the same vehicle and there was no space along the banks of the river to keep them, so we had to stack them up, one on top of each other until the bodies that were already burning had finished," he says.
"We even had to store some in the nearby forest."
The Nepalese government has been providing free firewood to families to help speed up the cremation process.
"It is part of our larger strategy to avoid the possible outbreak of disease which might be caused by bodies lying around," says Lakshmi Dahal, the spokesman for the Ministry of Home Affairs that has been co-ordinating the relief mission.
As the sun begins to heat up the day, large crowds filter through the ancient buildings that make up the temple complex.
People are coming here not just to cremate their dead, but to give thanks to Lord Shiva (a Hindu god) for having survived.
The temple itself has survived. Long cracks now snake their way down a few of its walls, but it was spared serious damage.
Tekra Limbu wishes the same was true for Kathmandu's other monuments.
He is here to cremate six members of his family, including his daughter and brother, who were on a family outing to the famous Dharahara Tower when it came crashing down on Saturday.
"They had just reached the top when the earthquake hit," he says as he and his relatives follow their procession of bodies.
"Four of them had just flown in from Singapore where they were working as policemen," he says.
Mr Limbu was trying to call his family all Saturday.
"Finally, when the security forces starting digging through the rubble that night, they found my brother's mobile phone which was still ringing," he says.
"They told me to come here and identify the bodies."
That night, he drove the 200km (125 miles) from his home in eastern Nepal to the capital, Kathmandu. He is stoic about his loss.
"I'm sad, but in a disaster like this, what can you do?" he says as he walks, grim-faced, towards the line of pyres being readied for his family.
A few metres along the river bank, agonising cries of pain overwhelm the quiet chants of priests and chimes of temple bells.
Shyam Kumari Bhandari is here to cremate her elder sister who died when her family's seven-storey guesthouse was violently shaken by the quake.
"She was on the top floor and we think she died of a heart attack," says Ms Bhandari, whose attention is now focused on another sister who has collapsed onto the temple steps, weak with grief.
For the last few days, the funeral pyres at Pashputinath have been burning from early morning until late into the night.
The soupy waters of the Bagmati River have become clogged with the detritus of cremation - charred pieces of wood and discarded marigold garlands.
The priests here hope this volume of death will soon end.
But they fear there are many more bodies still to come.
A pedestrian has been struck and killed by a car in Sussex.
[NEXT_CONCEPT]
At Kathmandu's Pashputinath temple, the morning air is heavy with birdsong and the smoke from funeral pyres.