Hundreds of pro-Palestinian activists are on board the flotilla, which aims to reach Gaza in defiance of an Israeli embargo on the territory.
The flotilla was originally made up of nine ships - from Turkey, the UK, Ireland, Greece, Kuwait and Algeria -carrying roughly 10,000 tonnes of aid, including cement, water purification systems and wheelchairs.
It was initially expected that the flotilla would set sail on Saturday, but it was delayed over the weekend due to mechanical problems.
The boats were forced to anchor off the coast of Cyprus this weekend.
Hamas, the de facto rulers of the Gaza Strip, have said that the flotilla was about to make history, sending "a strong message that the blockade imposed on the Gaza Strip ... will be broken".
Israel said the boats were embarking on "an act of provocation" with the Israeli military rather than providing aid, and that it had issued warrants to prohibit their entrance to Gaza.
It asserted that the flotilla would be breaking international law by landing in Gaza, a claim the organisers angrily denied.
Israel has said that it will intercept the boats and detain those on board in the port of Ashdod.