Yousseuf Sawani, executive director of the Gaddafi Foundation which charteredthe vessel, confirmed earlier that it had decided to divert the ship away from Gaza for safety reasons.
"It was unacceptable for us to enter into a confrontation and risk bloodshed," Sawani said.
"The aims of Amalthea have been achieved without bloodshed and the result is gains for the Palestinians."
He said earlier on Wednesday that eight Israeli warships had surrounded the Libyan aid ship, preventing it from continuing its journey to Gaza.
Amr el-Kahky, Al Jazeera's correspondent in El Arish, said the Egyptian foreign ministry had officially accepted a request from the ship to dock in El Arish.
"Offloading of the ship and loading [the supplies] onto trucks to travel to Gaza is due to take place tomorrow [Thursday]," he said.
The Amalthea is carrying 12 crew members and at least nine passengers, including six Libyans and one each from Algeria, Morocco and Nigeria.
A separate attempt to deliver aid relief and medical supplies to Gaza is also currently under way.
A convoy of 150 people, including "unionists, journalists and academics", is travelling overland in 25 vehicles from Jordan to the Egyptian Rafah crossing.
These challenges to the blockade come a day after Israel's military admitted mistakes in the May 31 attack on a flotilla of aid vessels trying to breach the blockade.
Nine pro-Palestinian activists, eight Turks and a dual US-Turkish citizen, were killed after Israeli soldiers boarded the lead ship Mavi Marmara.
Following an international outcry over the raid, Israel recently eased restrictions on the Gaza Strip, allowing some previously banned items into the territory.
But construction materials remain heavily restricted, Gazans have very limited freedom of movement, and Israel still enforces a naval blockade on the territory.