"They have been freed" and are on their way to Gaza City, Palestinian MP Kamal al-Sharafi told news agency AFP.
The Mr Sharafi is the deputy for Gaza and also heads the Al-Mezan rights group for which Kate Burton works.
Ms Burton, 24, was abducted at gunpoint on Wednesday along with her parents Hugh and Helen close to the Rafah border crossing into Egypt from the southern Gaza Strip.
Their release came shortly after Mr Sharafi had said there were "serious contacts in progress to release the hostages and we hope they will be freed in the next few hours".
More than a dozen foreigners have been kidnapped in Gaza since the summer but they have usually been released unharmed within a matter of hours after the captors submitted demands for jobs or payment to the Palestinian Authority.
Security sources had initially said the Burtons were abducted by the Black Panthers, a little-known offshoot of the ruling Fatah faction, but national police chief Alaa Hosni told reporters the kidnappers were unknown.
British authorities made clear they would not consider paying any ransom to secure the Burtons' release and left the case in the hands of the Palestinian Authority.
Three other Britons have been kidnapped since August in Gaza, including an employee of the United Nations who was freed after a gun-battle between the kidnappers and the security services.
The kidnappings have highlighted the Palestinian Authority's failure to control security in Gaza since Israel pulled out its troops and handed over control earlier in 2005.