An army spokesman confirmed the interception of the MV Dignite/Al Karama had been conducted without violence and said that the crew and passengers were put on an Israeli naval vessel headed to the southern Israeli port of Ashdod.
"IDF navy soldiers boarded the Al Karama in an effort to stop it from breaking the maritime security blockade on the Gaza Strip," a military statement said, indicating the move had come "after all diplomatic channels had been exhausted and continuous calls to the vessel had been ignored."
All 16 people on board the vessel had been offered food, drink and medical exams, it added.
Israeli sailors were bringing the yacht to Ashdod, where it and the occupants were expected to arrive before nightfall, the spokesman said.
The move to board the boat came some four hours after navy boats had surrounded the French-flagged yacht in international waters, 40 nautical miles off the Gaza shoreline, organisers said.
In a statement, the organisers denounced the navy's move to board the boat and urged the French government "to take its responsibilities and to protect the passengers, and to call on Israel not resort to violence."
"The deployment of Israeli military commandos to board this small boat... clearly demonstrates the military logic of Israeli policy, which speaks only the language of force," they said.
The boat had planned to arrive at Gaza's coast around midday on Tuesday, breaching Israel's blockade of the Palestinian territory.
But the Israeli naval forces that surrounded the boat made it clear that the activists would not be permitted to arrive in Gaza, calling on them to change course and head to the Egyptian port of El-Arish, an Israeli military source told AFP.
The yacht had set sail from the Greek island of Kastellorizo on Saturday evening following a troubled stay in Greece, after Athens imposed a ban on the departure of any ships involved in the flotilla.
As they embarked on the final stretch of their journey early on Tuesday, activists on board tweeted via @BateauGazaFr that they were still determined to reach Gaza.
"We're cleaning ourselves up a little bit before arriving. Morale here is like the sky and sea -- very good," wrote one French activist, while another added in English: "Gaza, off we go, stay connected!!!"
The yacht headed for Gaza despite Israeli warnings that it would intercept the ship -- the only boat remaining from a 10-vessel flotilla that had been due to sail for Gaza at the end of June.
In Gaza, Hamas spokesman Taher al-Nunu angrily denounced Israel's "Zionist piracy" and blamed the United Nations for not punishing Israel over its raid on a six-vessel flotilla that set sail in May 2010, led by the Mavi Marmara.
The raid left nine Turkish activists dead and prompted international criticism of Israel and a breakdown in ties with Ankara.
"This is a new act of Zionist piracy and the United Nations bears part of the responsibility because of its failure to punish Israel for its crimes against the Marmara, which encouraged it to continue to act in this aggressive and illegal way," Nunu told AFP.
"The international community must now take a clear stand on whether the siege on Gaza is legal and moral or not... and the answer will certainly be that it is illegal and immoral, which requires a serious stand against Israel that does not involve political hypocrisy and double standards."
Israel insists its blockade is both legal and necessary to prevent Hamas from obtaining funds and weapons in order to attack the Jewish state.
But Thomas Sommer-Houdeville, a French activist on board, told AFP the yacht was carrying nothing but a "symbolic message of peace and hope and love" and that Israel had no reason to intercept it.