"The doors suddenly flung open and within minutes the first batch of about 12 or so vehicles made their way from the Egyptian side to the Palestinians."
More than 100 vehicles followed the first batch into Gaza shortly afterward, he said.
Participants of the convoy are expected to spend the next 48 hours distributing the aid supplies.
Viva Palestina's arrival in Gaza followed violent clashes between Egyptian security forces, Palestinians and members of the convoy.
Hours before the convoy's arrival, an Egyptian soldier was shot dead during a clash with Palestinian protesters who had gathered along the border to protest a delay in the convoy's arrival.
Egyptian forces opened fire to disperse the stone-throwing protesters, and at least 35 Palestinians were wounded in the ensuing clash, according to Hamas officials.
Late on Tuesday, more than 50 people were wounded during a clash between Egyptian authorities and international members of the convoy.
The protests were sparked by an Egyptian decision to allow 139 vehicles to enter Gaza through the Rafah crossing, but requiring a remaining 59 vehicles to pass via Israel.
The convoy, led by George Galloway, a British MP, had already been delayed by more than a week, after he and a delegation of Turkish MPs failed to persuade the Egyptians to change their mind.
The convoy of nearly 200 vehicles arrived in Egypt's port city of al-Arish on Monday after a dispute with Cairo on the route.
But the arrival came after a bitter dispute between its organisers and the government, which banned the convoy from entering Egypt's Sinai from Jordan by ferry, forcing it to drive north to the Syrian port of Lattakia.
Al Jazeera's Amr El Kahky, who has been travelling with the convoy, said Viva Palestina's organisers had hoped to reach Gaza by December 27.
"We're talking about an almost 10 day delay. The convoy members are happy to have reached their destination," he said.
"Many of them have taken time off from their jobs in Europe and other areas and that's why they're happy to deliver the aid and go back home to resume their normal lives. So their jubilation is justified."
Israel and Egypt have severely restricted travel to and from the Gaza Strip since Hamas seized power there in June 2007, after winning Palestinian legislative elections in 2006.
The blockade currently allows only very basic supplies into Gaza.
The siege has severely restricted essential supplies and placed Gazans in a dire situation, made worse by Israel's military assault last winter that reduced much of the territory to ruins.
Galloway, the convoy organiser, said the mission represents only "a drop in the ocean" as long as the siege on Gaza continues.
"No number of convoys is going to solve the problems here," he told Al Jazeera.
"So we're not only trying to bring in aid, we're trying to show the world there is a siege.
"If there is anyone who doubted there is a siege on Gaza, they certainly aren't doubting it now after the events of the last 31 days with this convoy."