He said his previous two “births” were the day he survived an assassination attempt by Israeli agents in Jordan in 1997, and his actual birth in 1956.
Khaled Meshaal had not set foot in the Palestinian territories since leaving the West Bank in 1967.
His visit follows a ceasefire that ended days of violence between Hamas and Israel last month.
The Islamist militant group has governed Gaza since 2007.
Khaled Meshaal entered Gaza from Egypt at the Rafah border crossing, kissing the ground in celebration. Officials there said his wife had arrived late on Thursday.
In a statement to the media, he said: “I consider this moment my third birth, and I pray to God that my fourth birth will be the moment when all of Palestine is liberated.”
“Gaza has always been in my heart,” he said.
Khaled Meshaal is expected to visit the home of late Hamas founder Sheikh Ahmed Yassin, as well as that of Ahmed Jabari, the military commander killed in an Israeli strike last month.
Ahmed Jabari’s death marked the start of an eight-day Israeli offensive which Israel said was aimed at halting militant rocket attacks. Some 170 Palestinians and six Israelis were killed.
Hamas spokesman Sami Abu Zuhri said in a statement that Khaled Meshaal’s visit was “a fruit of the victory of the resistance over the occupation”.
A huge rally on Saturday is expected to be the centrepiece of his three-day tour.
Khaled Meshaal is scheduled to address the rally in Gaza City and will talk about the organization’s future strategy towards Israel.
He is also expected to discuss reconciliation moves with the Fatah movement, which Hamas removed from Gaza by force in 2007 after winning elections there. Fatah now rules parts of the West Bank.
In 2011, Khaled Meshaal and Palestinian Authority President Mahmoud Abbas – the Fatah leader – endorsed an Egyptian plan to reconcile the rival factions.
Although attempts to forge a Palestinian government of national unity have since stalled, Khaled Meshaal told Reuters ahead of his Gaza visit that “there is a new mood that allows us to achieve reconciliation”.
Khaled Meshaal was quick to praise Mahmoud Abbas’s recent success in upgrading Palestinian status at the United Nations to that of a non-member “observer state”.
In response to that move, Israel announced it would move ahead with building thousands of new homes in Israeli settlements in the West Bank and East Jerusalem.
Correspondents say Israel – which along with the US and EU considers Hamas a terrorist organisation – appears to be turning a blind eye to Khaled Meshaal’s visit.
Israeli foreign ministry spokesman Yigal Palmor said that Israel had no say over who entered Gaza from Egypt.
“We have no position on different individuals within Hamas,” he said, according to AP news agency.
“Hamas is Hamas is Hamas.”
On Thursday, Palestinian workers were setting up a stage for Saturday’s rally that included a replica of a type of rocket Hamas has fired into Israel. “Made in Gaza,” was written on it.
Khaled Meshaal was born in the West Bank in 1956. He moved to Kuwait after the 1967 Middle East war and later Jordan, where his involvement with Hamas began.
Khaled Meshaal survived an Israeli assassination attempt in Jordan in 1997 and was briefly jailed there, before being expelled and travelling to Qatar.
He became Hamas’s political leader in exile in 2004 when Sheikh Yassin was assassinated by Israel.
Khaled Meshaal ran operations from Damascus until February this year, when the unrest there prompted another move. He now bases himself in Qatar and Egypt.
Hamas was created in 1987 after the beginning of the first intifada – or Palestinian uprising – against Israel’s occupation of the West Bank and Gaza.
Under its charter, Hamas is committed to the destruction of Israel. But the group has also offered a 10-year truce in return for a complete Israeli withdrawal from territories it occupied in 1967.
Khaled Meshaal
1956 – Born in Silwad in West Bank
1967 – Moves with family to Kuwait after Six Day War
1971 – Joins Muslim Brotherhood
1987 – Hamas created
1991 – Moves to Jordan after Iraq invades Kuwait. Runs Hamas fundraising
1997 – Survives Israeli assassination attempt
1999 – Expelled from Jordan. Moves to Qatar
2001 – Moves to Syria
2004 – Named Hamas political leader after assassination of Sheikh Ahmed Yassin
2012 – Leaves Damascus for Egypt and Qatar
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