The three ships will then travel to the waters off Athens and Crete to rendezvous with the other six, before making the four-day journey to Gaza.
Al Jazeera's Anita McNaught, reporting from Istanbul, said Turkey has high hopes for the flotilla as Gaza is an issue close to their hearts.
"It has been a very emotional evening in Istanbul. The issue of Gaza moves Turks more than any other single issue," McNaught said.
"It has severely coloured the government's relationship with Israel and many Turks feel a community spirit and sense of responsibility for the situation in Gaza."
Mohammad Sawalha, the vice president of the international committee to break the siege of Gaza, one of the organisers of the mission, told Al Jazeera that a global movement, made up of people who want to send the message that the situation in Gaza is unacceptable, was growing.
"We are trying to send a message to everybody that the situation in Gaza will not go on," Sawalha said.
"No one can accept what is going on now in Gaza - preventing people from having the food and medicine they need. This is a crime."
The convoy is from the UK, Ireland, Algeria, Kuwait, Greece and Turkey, and is comprised of 800 people from 50 nationalities. It is made up of three cargo ships and five passengers boats.
A senior Israeli official has warned the activists that their flotilla of cargo ships and passenger boats will be stopped from entering Gaza.
Naor Gilon, a deputy director general at the foreign ministry, said the action would be a "provocation and breach of Israeli law".
A statement from Israel's foreign ministry said it had "no intention of allowing the flotilla into Gaza" but has not elaborated on what measures could be used to stop them.
Representatives from six organisations, including the European Campaign to End the Siege in Gaza (EGESG), said they were determined to enter the area regardless of pressure from Israel.
"Israel should not be under any illusion whatsoever that their threats or intimidation will stop us or even that their violence against us will stop us," Huwaida Arraf, from the Free Gaza Movement, said.
Kahel Mazen, from EGESG, added: "If they [the Israelis] choose to resort to destruction and death, our mission is to try to open a window of hope for the people of Gaza."
Israel says the blockade aims to prevent Hamas, the political movement that controls Gaza, from acquiring weapons or materials that could be used for military purposes.
For the majority of Gaza's population of 1.5 million people, the result has been impoverished living conditions.