"There was no violence or injuries amongst the soldiers or crew ... and no shots were fired," the statement said.
Jacky Rowland, Al Jazeera's correspondent in Ashdod, said the Rachel Corrie arrived at the port, escorted all the way by Israeli military vessels.
"The aid will be taken off and inspected," she said.
"It is not clear how much of it will be taken to Gaza. We can expect the passengers to be deported fairly promptly."
Activists on board the Malaysia-funded Irish ship were attempting to break the siege of Gaza imposed by Israel, five days after its troops killed nine activists while raiding a flotilla of aid ships carrying humanitarian aid for the coastal Palestinian territory.
Israeli naval vessels trailed the Rachel Corrie for several hours before boarding it. The ship's radar was jammed, cutting off all radio communication.
Miri Eisin, a spokeswoman for the Israeli government, told Al Jazeera that the vessel was boarded by soldiers at the edge of the maritime zone of Gaza in agreement with those on board.
"The people on board will be taken care off in accordance with Israeli law, as they have approached Israel illegally, so they will be asked to leave voluntarily," she said.
Eisin said the cargo would be offloaded at Ashdod and then transferred to Gaza.
Binyamin Netanyahu, the Israeli prime minister, said naval forces involved in Saturday's operation had followed exactly the same procedures as they had done earlier in the week, but the difference lay in the attitude of the activists on board the vessel.
"We saw today the difference between a ship of peace activists, with whom we don't agree but respect their right to a different opinion from ours, and between a ship of hate organised by violent Turkish terror extremists ... waiting for our soldiers on the deck with axes and knives," Netanyahu's office cited him as saying.
On the other hand, Mukhriz Mahathir, head of the Perdana Global Peace Organisation, a Malaysian non-governmental organisation that sponsored the Rachel Corrie, said people would be willing to contribute to further aid ships.
Al Jazeera reports from London on protests against the Israeli raid and embargo on Gaza
"These actions have finally succeded in raising lots of awareness," he said.
"But for the moment, we are upset that these aid goods have not reached their destination."
The Rachel Corrie, which carried 11 activists and eight crew members, is named after an American womanwho was killed by an Israeli military bulldozer in the Gaza Strip in 2003, while protesting against a house demolition.
Pro-Palestinian activists on board the ship had earlier said they were determined to press ahead towards the Gaza coast, despite the Israeli warnings.
"We are not afraid and we are all advocating non-violence… and we will just sit here and go if they insist on commandeering our boat and forcing us into Ashdod," Mairead Maguire, an activist and Nobel Peace laureate aboard Rachel Corrie, said before radio contact with the ship was lost.
The Israeli military had cautioned that troops would consider storming the ship, if it continued its journey towards Gaza.
In a statement, the Israel navy warned the ship that it was "approaching an area of hostilities which is under a naval blockade. The Gaza area, coastal region and Gaza Harbour are closed to all maritime traffic."
Avital Leibovich, an Israeli military spokeswoman, told Al Jazeera that the military had a government directive to make sure the ship does not reach Gaza.
Al Jazeera's Nicole Johnston, reporting from Gaza, said the Rachel Corrie had hundreds of tonnes of aid, including medical supplies, wheelchairs, cement, building materials and even note pads for children.
Speaking to Al Jazeera on Saturday, Chris Guinness, a spokesman for UNWRA, the United Nations Palestine refugee agency, underscored the need for Gaza's land and sea blockades to be lifted.
Israel's raid has led to protests in many nations including in the French capital Paris
"The World Health Organisation needs 20 million dollars worth of aid to enter Gaza, there is 44 per cent unemployment and education is in crisis," he said.
"We are turning thousands of five and six year olds away from our schools [and] 39,000 children in Gaza are not receiving United Nations education because we cannot get our building materials in.
"We also want to see exports coming out of Gaza. It is already 80 per cent aid dependent. What we don't want is to make it more aid dependent."
The developments surrounding the Rachel Corrie came as the UN human-rights chief said that Israel could face prosecution for Monday's flotilla raid, and that she was following requests for a referral to the International Criminal Court [ICC] in the Hague.
"I am following very closely the very many calls that come particularly from civil society and from all the people who are suffering in Palestine for that kind of action to be taken," Navi Pillay, the high commissioner for human rights, said on Saturday in Kampala, Uganda, where she was attending the ICC's ongoing review conference.
She said she believed Israel's blockade of Gaza violates international law.
"International humanitarian law prohibits starvation of civilians as a method of warfare ... It is also prohibited to impose collective punishment on the civilian population, so it is [for those reasons] that I have consistently reported to member states that the blockade is illegal and must be lifted," Pillay said.
"Even if it is demonstrated that the blockade is legal under international law, Israel's current military operations against the flotilla must be analysed from the perspective of its obligation to allow humanitarian aid to be brought into the Gaza Strip."