After the men were pardoned on Monday, they flew to Istanbul and then on to Sweden to arrive just before midday on Friday.
The men hugged relatives, received flowers and were photographed with family members.
“We feel good and are incredibly relieved,” they told the TT news agency.
Persson and Schibbye will speak further at a press conference in Stockholm on Friday afternoon.
After ten minutes at the airport, the Swedes left in a car. Ambassador Jens Odlander, who accompanied the pair from Istanbul, joined the two in interviews but left separately.
Schibbye and Persson were arrested in Ethiopia’s Ogaden region last year in the company of what the government claimed were rebels from the Ogaden National Liberation Front (ONLF).
The two had reportedly entered Ethiopia to investigate the activities of a company affiliated with the Swedish oil firm Lundin Petroleum.
The pair was detained after illegally crossing the border from Somalia, and after a long and controversial trial were jailed for 11 years by an Ethiopian court in December 2011, having been found guilty of supporting terrorism and entering the country illegally.
The pair was pardoned on Monday in connection with the Ethiopian New Year, when the country traditionally pardons prisoners.