Krishna Upadhyaya and Gundev Ghimire, the two British human rights researchers detained in Qatar for almost nine days, have reportedly been released from custody, but have not yet left the country.

"I received a call from Krishna at about 1am [UK time]. He said he had just been released," Upadhyaya's wife, Sarita Poudyal, told the Guardian. "He sounded very happy. He was completely unaware of all the work they had been done to release him. He told me he would be leaving Qatar in two days."

Ghimire's wife, Bandana Koirala, said she had communicated with her husband on Facebook. He confirmed he had been released and asked her to convey the message to all his friends and family.

"I can't explain how I feel right now," said Koirala. "It's been a very difficult situation for all the family. Now that I know he has been released I feel able to wait a few more days until he comes home."

Upadhyaya and Ghimire went missing in Qatar on 31 August. After almost a week without any official statement on the men's whereabouts, the ministry of foreign affairs in Qatar announced on Sunday that the men had been arrested and were "being interrogated for having violated the provisions of the laws of the state of Qatar".

According to their employer, the Global Network for Rights and Development (GNRD), the men were in Qatar researching a forthcoming report on the working and living conditions of Nepalese migrant labourers.

Evgenia Kondrakhina, the chief executive manager of GNRD, said: "Tomorrow Krishna and Gundev will need to go to the police to get their gadgets back after all data will be erased from them … Once they finish with the police they will contact us to confirm when we can reserve tickets for them … We will now concentrate on organising their transfer back home as soon as possible."

A spokesperson for the British embassy in Qatar said: "The British embassy can confirm that Krishna Upadhyaya and Gundev Ghimire have been released."

The ministry of foreign affairs in Qatar could not be reached for comment.