Fast bowler Southee and batsman Nicol had been confined to Colombo even as the squad travelled to Kandy on Tuesday ahead of their group D match against Bangladesh in Pallekele on Friday.
Southee was briefly admitted to a Colombo hospital to be kept under observation for signs of dehydration, but both players were declared fit to travel to Kandy on Wednesday.
"The players have shown good improvement. They are currently travelling from Colombo to join the team in Kandy," team spokesperson Ellery Tappin said by phone from the hill town.
Former captain Daniel Vettori, who had also suffered a stomach bug, recovered sufficiently to travel with the rest of the squad.
"Dan's still pretty low in terms of energy levels but getting back up," New Zealand coach Mike Hesson said.
Pakistan are the third team in group D, from which the top two will advance to the Super Eights round.