The team plans to complete its fact-finding mission in a week, but Goldstone said they were likely to return within a month, before presenting a report in August.
Goldstone's team plans to meet witnesses and victims of alleged violations, non-governmental organisations and UN agencies in Gaza.
Goldstone is former chief prosecutor at the International Criminal Tribunals for the former Yugoslavia and Rwanda and lead a public inquiry into intimidation and violence leading up to South Africa's first post-apartheid elections in 1994.
Ghazi Hamad, a representative of Hamas, and local UN officials met the investigators at the Rafah crossing.
"They have already met government officials, mostly from the ministry of health here," Al Jazeera's Ayman Mohyeldin, reporting from Gaza City, said.
"They have been presented with nearly two hours of video material prepared by the government, including testimonies of witnesses and those that suffered."
"Over the course of the next few days ... they will see for themselves the wanton destruction across the Gaza Strip. They will visit areas where alleged war crimes have taken place and hear directly from the Palestinian people."
Israel accuses the UN's mission of being biased.
"They have been instructed to prove that Israel is guilty and we will not collaborate with such a masquerade," Yigal Palmor, Israel's foreign ministry spokesman, told The Associated Press news agency.
Palmor said Israel had no plans to co-operate with the investigation.
In May, Goldstone had said he hoped to visit Gaza and southern Israel and hold public hearings on whether war crimes had been committed.
Fawzi Barhoum, a Hamas official, welcomed the investigation in a statement.
"We hope to see the leaders of the Zionist enemy brought to justice as soon as possible as war criminals in the international courts," he said.
During the 22-day conflict which ended in January, 1,417 Palestinians were killed, including 926 civilians, according to Palestinian officials.
But Israel says that the number killed is considerably lower, and that only 295 of the dead were civilians.
International human rights groups, including Amnesty International, have called for a credible and independent investigation of Israel's conduct in Gaza.
They specifically asked for inquiries into the destruction of residential areas and the use of artillery shells containing white phosphorous, which can cause severe burns.
Israel, which conducted an internal investigation by its armed forces last month, says it found no evidence of serious misconduct by its troops.