Johan Persson and Martin Schibbye.
Kjell Persson, the father of Johan Persson, told Swedish news agency TT that his son and Martin Schibbye had left Addis Ababa overnight but were now resting in private before returning home.
"I have been in contact with Johan this morning," Persson said, refusing to disclose where his son was.
"They'll rest up for a few days first … then there will be a press conference at [Stockholm airport] Arlanda and we'll be there too," he said.
Swedish media said the remarks suggested that the pair were not yet in the Scandinavian country.
A statement from the journalists' spokesperson said they needed time to recuperate after their ordeal.
"After 14 months in a jail where it's never quiet, dark or still, Johan and Martin have asked for a little breathing room. They want to have a chance to eat, sleep, read the Swedish news and see a doctor before they come home to meet the press and all the others who've been waiting for them," the statement said.
"They've been really strong through it all," Kjell Persson told TT, but he warned of the risk that, once the two men relax, they may be hit by the full emotional impact of their ordeal.
Dinner at the embassy
Swedish ambassador Jens Odlander told Swedish Radio late Monday that Schibbye and Persson had had dinner with him at the embassy in Addis Ababa before the three boarded a plane together.
Ethiopia on Monday pardoned and freed the freelance reporters after they served 14 months of their 11-year jail sentence for "supporting terrorism".
Schibbye and Persson were arrested with rebels from the Ogaden National Liberation Front (ONLF) on July 1, 2011 after illegally entering from Somalia.
They were in the remote southeastern region of Ogaden, populated mainly by ethnic Somalis, to investigate the activities of a company affiliated with the Swedish oil firm Lundin Petroleum.
The case had drawn heavy criticism from rights groups. The journalists were convicted under Ethiopia's anti-terror law, which critics have called vague and indiscriminate. – Sapa-AFP