Hamdallah crossed the border with dozens of ministers and officials from the West Bank-based PA into the Hamas-run coastal enclave at around noon.
The Islamists have controlled Gaza since a 2007 split but recently agreed to hand over civilian power to a unity government.
"The government began to exercise its roles in Gaza from today," Hamdallah said at a press conference at the crossing.
"We return to Gaza again to end the division and achieve unity."
He was welcomed by thousands of Gazans, with hopes that this reconciliation plan can avoid the problems that wrecked several previous attempts.
Hamdallah's entry was delayed by around half an hour because of disputes between PA and Hamas security men, a security source said.
Hamas politicians and members of the premier's Fatah faction greeted Hamdallah on arrival.
He is expected to meet Hamas's overall leader Ismail Haniya and its Gaza chief Yahya Sinwar later Monday, and chair a cabinet meeting on Tuesday.
The event is meant to be the first significant step in a transfer of powers.
Hamas ousted the PA in 2007 after a near civil war, but recently agreed to dissolve what has been seen as its rival administration and make way for a unity government.
Palestinian president Mahmud Abbas's PA is the internationally recognised Palestinian government and supposed to steer its people to an independent Palestinian state.
Hamas, blacklisted as a "terrorist" group by the European Union and the United States, won a landslide victory in 2006 Palestinian parliamentary elections.
It ousted Fatah from Gaza the following year after wrangling over the formation of a new government degenerated into bloody clashes.
Abbas's limited power has since been confined to the West Bank which is under Israeli military occupation and located, at its nearest point, 40 kilometres (25 miles) from the Israel-Gaza border.
More pragmatic Hamas?
The logistics of the visit are themselves an indication of Palestinian divisions and challenges.
Arriving by road from Ramallah, about 70 kilometres (44 miles) away in the West Bank, Hamdallah's convoy crossed Israel and then transited the fortress-like Erez crossing into Gaza before passing a Hamas checkpoint.
Hamas last month finally agreed to the PA's return to Gaza, under pressure from the enclave's powerful neighbour Egypt.
The group was squeezed by Abbas, who stopped paying Israel for electricity it supplies to Gaza, resulting in devastating power cuts.
For Gaza's two million residents, the hope is to see an improvement in their miserable living conditions in the overcrowded and impoverished territory.
Battered by three wars with Israel since 2008, Gaza is under Israeli and Egyptian blockade and suffers from severe water and electricity shortages, an economic slump and unemployment of more than 40 percent.
Care for young
Abu Musa Hamduna, a 42-year-old Gazan, welcomes the return of central government.
"We call on it to take care of the young -- this is the most important -- and to resolve the electricity crisis and improve the living conditions of the people of Gaza," he said.
Experts say that the prospect of social unrest among disgruntled Gazans was a factor in Hamas's willingness to reconcile with Fatah, along with its growing isolation and perhaps a new pragmatism in its leadership.
Hamas and Fatah, which dominates the PA, have both expressed confidence that the latest unity initiative will fare better than the failures of the past.
But scepticism remains rife, with many observers suspecting Hamas of a tactical manoeuvre to improve its position.
They doubt Hamas will cede its security control over the strip to the PA, and see major challenges for Abbas in finding a future for the thousands of public workers recruited by Hamas over the past decade.
Particularly thorny issues include the potential future of Hamas's military wing.
The Hamdallah delegation's visit is seen as largely symbolic and preparing the ground for further talks, probably in Cairo.
The outcome will determine the Palestinians' acceptance on the international stage.
The PA recognises Israel, but that appears to remain out of the question for Hamas.
Israeli construction minister and former general Yoav Galant says everything depends on Hamas accepting Israel's existence and ending armed struggle.
"If the answer is positive, we can talk about a lot of things," he says. "If it is negative, nothing has changed and all this is a deception."
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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