The 27 activists on board the two ships would be identified and questioned by immigration authorities and then taken to Ben Gurion airport near Tel Aviv to be flown back to their home countries, the report said.
It noted that one of the activists was an Israeli national, who it said would be sent home after being questioned.
An Israeli security source said earlier there were "no injuries" during the boarding process, which occurred just minutes before the start of the Jewish sabbath.
"The Israel navy soldiers operated as planned, and took every precaution necessary to ensure the safety of the activists on board the vessels as well as themselves."
The boarding came after the two ships refused to heed calls to change course, prompting military Chief of Staff Benny Gantz to order their interception.
"The IDF Chief of Staff ordered the navy to board the vessels should they refuse our radio requests," the military spokesman's unit tweeted, using the identifying hashtag "provocatilla."
Dublin-based organisers of the Irish boat said they had been contacted Friday afternoon by those on board to say they were being "rapidly" approached by two Israeli warships, with first radio contact made some 15 minutes later.
Shortly afterwards, the Canadians also confirmed radio contact had been made, in a posting on Twitter. "Israeli war ship: 'What is Tahrir's final destination?' Our response: 'The betterment of mankind'," they wrote.
The last time a boat tried to reach Gaza was in July, when a French-flagged yacht, the last remaining boat of an earlier flotilla, was intercepted by the Israeli navy some 40 nautical miles off the coast.
The Irish boat was carrying 15 passengers and crew members. The Canadian boat had 12 people on board, five of them journalists, and a cargo of $30,000 (22,000 euros) worth of medical aid and letters of solidarity, organisers said.
Denis Kosseim, a Montreal-based spokesman for the Canadian Boat to Gaza campaign had earlier told AFP the passengers and crew had agreed not to put up a fight if Israel moved to intercept the boats.
"Everyone has signed a document in which they pledged not to put up any resistance should they be boarded by Israel," he said.
On Thursday evening, Israeli warships came within six nautical miles of the two vessels, sparking unfounded fears they might board the ships overnight.
Activists organised a major attempt to break the Israeli blockade in May 2010, when six ships led by the Turkish Mavi Marmara tried to reach Gaza.
Israeli troops stormed the Marmara, killing nine Turkish activists and sparking a diplomatic crisis with Ankara, which expelled the Israeli ambassador and has cut military ties with the Jewish state.
Earlier this year, a second flotilla tried to reach Gaza, but several ships were sabotaged -- which activists blamed on Israel. Only the French-flagged yacht, the Dignity, was able to attempt the last leg of the journey but was stopped by the navy and those on board were deported.
Israel says its blockade is necessary to prevent weapons from entering the coastal territory, which is run by the Islamist Hamas movement.
Two months ago, a UN report on the flotilla raid accused the Jewish state of acting with "excessive force" but found that its naval blockade on the coastal territory was legal.