A previously unknown Palestinian group, the Brigades of the Mujahidin, said on Friday it had freed the hostages, kidnapped two days earlier, and it called on Britain and the rest of Europe to put pressure on Israel.
In a video released to the media by the group, a masked gunman stood next to Kate Burton, 25, as he listed demands and threatened that more foreign hostages would be taken if they were not met. Releasing the Burton family was a "gesture of goodwill".
Burton and her parents, Hugh and Helen, had been kidnapped on Wednesday in the chaotic southern town of Rafah, on the border with Egypt.
A Palestinian security official said on Friday: "They are secure and in good hands." A British official said he had been informed of their release and was waiting for them at a meeting point in Gaza City.
Witnesses to the kidnapping said about seven men, armed with automatic rifles, pulled over a car used by Burton and her parents, who were visiting her. The Britons were bundled into a white vehicle that sped away.
Nothing was heard from the kidnappers for two days, whereas other foreigners taken hostage in Gaza have usually been released within hours.
There has been a rash of kidnappings in Gaza since Israel withdrew from the coastal territory in September after 38 years of occupation, a move welcomed internationally as a potential spur to peace but which left the Palestinian Authority struggling for control.
The kidnapping of the three Britons, and the international attention that it drew, came as a fresh embarrassment for Mahmoud Abbas, the Palestinian president.
A Dutchman and an Australian, teachers at a school in Gaza, were briefly abducted last week by the Popular Front for the Liberation of Palestine, which demanded that its leaders be released from jail.
Burton worked for Al Mazen, a group that documents alleged Israeli abuses of Palestinian rights, and her abduction prompted popular protests in Gaza.