Lauren Booth, a sister-in-law of former British Prime Minister Tony Blair, is among the activists with the "Free Gaza Movement" on board the two wooden boats.
"Now, Israel claims that Gaza is no longer occupied, yet Israeli forces patrol Gaza's borders by land, seas and air so the point of this mission is to get two ships to sail from Cyprus into Gaza to challenge this illegal occupation," she said.
Israel ended its occupation of Gaza in 2005, but when Hamas militants seized power two years later, the international community cut most aid to the territory except for humanitarian supplies.
Israel, which has been the target of repeated rocket attacks and incursions from militants in Gaza has effectively sealed off the area. The economy of Gaza has collapsed as a result of the near total isolation.
Israel, the United States and the European Union consider Hamas a terrorist organization for its continued refusal to recognize Israel or renounce violence.
In 1988, the Palestinian Liberation Organization staged an unsuccessful effort to sail from Cyprus to the Israeli port of Haifa. The ship, named the Sol Phryne, was damaged in a mine attack in the Cypriot port of Limassol.