Gareth Jones, 69, was reported missing with his brown cockapoo dog on Saturday (January 16) having not been seen since 1pm, police said.
A major search was launched to find him last night and continued today.
A spokesman said: “Officers investigating the matter have viewed CCTV from the area where he was last seen, and believe it shows Gareth and his dog sadly getting swept out to sea.
“Despite extensive searches involving Sussex Police, HM Coastguard, lifeboat crews and search and rescue volunteers, Gareth nor his dog have been found.
“Coastguard and lifeboat crews have now been stood down from the search, but police officers and volunteers are continuing to search the coastline.
“Sussex Police would like to thank all of those involved with the search, including members of partner agencies and the many volunteers who have offered support.”