Officials in the northern Malian town of Gao said on Sunday that the nine Germans, four Swiss and a Dutchman, abducted by a suspected Islamist group, were released in the town of Tessalit in the northeastern region of Kidal.
A source close to the negotiations with the kidnappers also confirmed that "the hostages are today free."
Germany's public ZDF television reported that the release followed a payment to the kidnappers Saturday of a ransom, although the station said that the money did not come from the German government.
However, another German public television station, ARD, cast doubt on ZDF's report, although it also speculated that a release was imminent.
ARD said Juergen Chrobog, a German foreign ministry state secretary who is Berlin's point man on the crisis, had telephoned his superiors to assure them that the ZDF news "did not correspond" with his own information.
"We have high hopes. The fact I have come with a medical plane shows we are confident"
German foreign ministry
The German and Swiss foreign ministries both refused to comment.
According to ZDF, a German air force transport plane is to fly the missing tourists from a military airport in northern Mali to the capital Bamako where they would undergo medical checks.
The officials in Gao also said the hostages would be returned on board the Transall, which an Agence France Presse journalist saw at Gao airport.
Earlier, a Malian military plane had landed at Gao only to take off a short while later for Tessalit with troops on board, military and airport sources said.
"It's rare for a military plane to go there," a military source told AFP.
ZDF said Chrobog played a direct role in negotiations with the kidnappers by satellite telephone, one of the hostages acting as an interpreter.
Chrobog had spoken confidently of a swift and peaceful end after flying in earlier Sunday to Bamako, his third visit to the region.
"We have taken all the necessary measures" for the evacuation, he said. "I cannot tell you if they will be released tonight, it could take a bit longer.
"But we have high hopes. The fact I have come with a medical plane shows we are confident."
ZDF said he would accompany the tourists home, possibly as early as Sunday evening, on the Transall plane, which is medically equipped.
A total of 32 Europeans were seized in southern Algeria earlier this year, but 17 were freed in a raid by Algerian special forces in May, and one German woman, Michaela Spitzer, 46, is thought to have died from heat exhaustion and been buried in the desert.
A German poster shows the hostages
Previous reports had suggested the captors were demanding a ransom of $5.5 million for each person but Germany was unwilling to pay, fearing it would encourage copycat abductions.
Amari Saifi, an Algerian army renegade known as Abderrezak the "Para", had been identified as the head of the abductors.
He heads a faction of the Salafist Group for Preaching and Combat (GSPC), an Islamic extremist Algerian group reportedly linked to the al-Qaida network.
The hostage takers were believed to be holding out in the vast desert wastelands of northern Mali, although their exact location is not known.
German security agents had deployed throughout the desert wilderness where the abductors are reported to have brought the Europeans, seized more than four months ago.
The condition of the group is not known, but one of the Swiss hostages is diabetic, according to diplomats, while others have been reported to be unwell.