Nick Hancock will break the 42-day overall occupation record, set by members of Greenpeace in 1997, having been on the rock 260 miles out into the Atlantic for 43 days.
He broke the current 40-day solo occupation record set by Tom McClean on Tuesday.
He celebrated achieving that by popping a small bottle of champagne while also sending a tweet with a message to veteran adventurer Mr McClean, of Morar, who held the solo record for 29 years. Mr Hancock's message read simply: "Sorry Tom."
Mr McClean's wife Jill has since sent a message saying: "Tom is busy at present planning his ventures and has asked me to say 'well done' to Nick and to keep up the good work!" Cruise boat operator Kilda Cruises say expected favourable weather at the weekend mean they plan to take Mr Hancock off the rock on Saturday.
Last year Mr Hancock, a chartered surveyor from Ratho near Edinburgh, had planned to stay on the rock, which is 100ft wide and 70ft high, for 60 days. But he conceded defeat in face of the high seas that were running.
Two weeks ago he feared he may have to abandon his challenge early after losing vital supplies in a storm.
It was in 1997 that three Greenpeace activists set the 42-day-long occupation record, renaming Rockall the new micronation of Waveland in protest at oil exploration in the area.
Mr McClean, a former SAS soldier, went to the rock in 1985 and stayed for 40 days.