Dutch foreign minister Bert Koenders said the pair "are doing relatively well under the circumstances".
Earlier in the day, the radio announced that Derk Bolt and Eugenio Follender had been freed after they were reportedly abducted over the weekend while working in the northeastern Catatumbo region.
Then they were shuttled from safe house to safe house before eventually taking refuge in the jungle.
"It was very hard", he added, "but the people who captured us were very friendly and treated us with great respect".
The ELN, now engaged in exploratory talks with the Colombian government in Ecuador, said on Wednesday they would release the Dutch journalists to a humanitarian commission if they determined that one of their units had kidnapped them. They are now facing a journey back through the jungle.
But the Dutch embassy in Colombia told the BBC they had no information about the claim, which could not be verified.
"In the rural area of Catatumbo, two Dutch journalists were handed over to the ombudsman by the ELN", they confirmed in a tweet with photos depicting the exchange.
Bolt and Follender work for Spoorloos, a programme on Kro-Ncrv TV that helps Dutch people trace their biological relatives around the world.
"We are incredibly happy and relieved", the show said in a Facebook post. "We apologize and reiterate that the two foreigners are in flawless condition", it tweeted.
People protest against the kidnapping of Dutch journalists Derk Johannes Bolt and Eugenio Ernest Marie in Bogota, Colombia June 21, 2017.
The ELN is Colombia's last major guerrilla army with about 1,500 troops.
Their capture was the latest in a series of incidents that officials feared could disrupt peace talks between the ELN and the government.
The ELN in a statement said the journalists were detained preventively because they had entered a conflict zone where Colombia's military often operates covertly.