The workers - four Britons and one French citizen - had been released into the care of the authorities in Eritrea, she said.
Mrs Beckett said they were safe and were "broadly all in good health".
But eight Ethiopian staff who had been with the group when they were captured had still not been released, she added.
The freed hostages were being cared for at the British Embassy in Eritrea's capital Asmara, she added.
Families informed
Whitehall officials later said the released five had been seen by a doctor and did not appear to have been mistreated.
They have been named as the Foreign Office's Peter Rudge and Jonathan Ireland, who both worked at the British Embassy in Addis Ababa; Malcolm Smart and Laure Beaufils, of the Department for International Development in Addis Ababa; and Rosanna Moore, wife of the head of the British Council in Addis Ababa.
It is hoped they will come back to the UK "shortly" but there is as yet no timetable for their return, said a Foreign Office spokesman.
The party were apparently on a sightseeing tour when they were abducted on 1 March.
BBC security correspondent Frank Gardner said that he expected the five released Britons would be debriefed in Asmara, and that this should provide more information about who kidnapped them and what conditions they were held in.
"We have informed the families of all five who were, of course, very relieved and are looking forward to being reunited," Mrs Beckett said.
"We continue to be concerned about the wellbeing of the Ethiopians who were taken at the same time as the British group," she said.
Embassy officials had "worked tirelessly" to help secure the group's release, she added.
She also thanked the authorities in Ethiopian and Eritrea for their "exceptional assistance".
A spokesman for Prime Minister Tony Blair welcomed the release of the hostages.
BBC diplomatic correspondent Paul Adams said the Foreign Office had insisted that no-one was paid for the hostages' release.
'Wrong place'
Shadow Foreign Secretary William Hague also welcomed the "wonderful news".
According to reports, Ethiopia's information minister Berhan Hailu said the search would continue for the citizens of his country who remained missing
"We don't have any information about them. We are very concerned," he told Reuters news agency.
"They should be released unconditionally and as soon as possible."
One of the Land Rovers driven by the group was recovered at the weekend in the village of Hamedali, in the Afar region.
The region straddles the border of Ethiopia and Eritrea.
Relations between the two countries have been strained since Eritrea gained independence from Ethiopia in 1993 after a 30-year guerrilla war.
On Monday, Ethiopia's Prime Minister Meles Zenawi said the workers were people who had "not done anything to hurt anyone".
"I do not believe these people were targeted. They were in the wrong place at the wrong time," he said.
He spoke of the kidnappers having taken "a step too far", saying they "need to find a way to redress their steps in a way that does not affect their interests".
Un groupe d'employés de l'ambassade britannique enlevés dans le nord de l'Éthiopie il y a douze jours ont été relâchés selon Margaret Beckett, secrétaire au '''' (minstre des Affaires étrangères). Les employés - quatre sujets britanniques et un citoyen français, ainsi que l'équipe éthiopienne travaillant avec eux, avaient été enlevés en Érythrée a-t-elle annoncé.

Le groupe était apparement en excursion lorsqu'il fut enlevé le 1 mars dernier. M Beckett a aussi indiqué que tous les enlevés étaient sains et saufs et : .

Le groupe fut porté disparu le 1 mars lors d'un voyage touristique pour visiter les sites géologiques de la région Afar, dans le nord du pays. Deux véhicules appartenant au groupe furent trouvés plus tard dans un village du nord-est appelé Hamedali. Ils étaient criblés de balles, mais contenaient toujours bagages et téléphones mobiles.

La région Afar chevauche la froniètère entre l'Éthiopie et l'Érythrée. Le Premier ministre éthiopien, Meles Zenawi, avait annoncé lundi que les autorités éthiopiennes avaient  de l'endroit où les otages étaient détenus.

M. Zenawi avait déclaré que le personnel de l'ambassade n'avait pas été visé en particulier et avait suggéré que cet enlèvement était peut-être une erreur. Hamedali est un point de départ pour les touristes visitant les formations géologiques uniques de la Dancalie, comprenant la fameuse région des lacs salés. La région constitue l'une des plus chaudes et inhospitalières terres de la planète. Les visiteurs sont encouragés par le gouvernement à se déplacer en convois avec une escorte armée en raison de la présence de rebelles et de bandits. Des témoins ont indiqués qu'environ 50 hommes sont tombés sur le village et ont forcé les étrangers à traverser la frontière érythréenne à pied.