Israel and Hamas announced an agreement on Tuesday to exchange more than 1,000 Palestinian prisoners for an Israeli soldier held captive in Gaza for five years, a deal brokered by Egypt that seemed likely to shake up Middle East politics at a time when the region is immersed in turmoil.

Prime Minister Benjamin Netanyahu of Israel told his nation in a live address on television that the soldier, Staff Sgt. Gilad Shalit, who was captured in June 2006 at the age of 19, could be home “within days,” ending what has been widely seen in Israel as a national trauma.

In Damascus, Syria, Khaled Meshal, the political leader of Hamas, said in a televised address that the negotiations had been “very, very difficult” and called the deal “a national accomplishment” that augured well for the Palestinians, who he said hoped to “cleanse the land, and liberate Jerusalem, and unite the Palestinian ranks.”

It was unclear what drove the two to accept a deal that had been on the table for years. But both stand to benefit politically and had reasons to distract attention from the efforts of Mahmoud Abbas, president of the Palestinian Authority, as he circles the globe seeking votes for his bid to gain United Nations membership for a state of Palestine.

Egypt played a central role in the deal, helping bolster its international standing at a time of growing internal political strife as well as strains with Israel, which has seen its relationship with Egypt deteriorate since President Hosni Mubarak was toppled in February. Just last month, an Egyptian mob attacked Israel’s embassy and its diplomatic staff was evacuated.

Mr. Netanyahu, whose cabinet voted 26 to 3 in favor of the prisoner swap, said he felt it important to move on the deal now, given what he called the “storms” in the Middle East.

“With everything that is happening in Egypt and the region, I don’t know if the future would have allowed us to get a better deal — or any deal at all for that matter,” he said. “This is a window of opportunity that might have been missed.”

An Israeli official said on Tuesday that Israel had sent a letter of apology to Egypt for the deaths of several of its troops by Israeli forces chasing Palestinian militants into Sinai in August.

Many aspects of the agreement were not revealed, including the names of important Palestinian prisoners expected to be released. But Israeli journalists said after an intelligence briefing that Marwan Barghouti, a top leader of the Fatah group sentenced to five life terms and seen as a possible successor to Mr. Abbas, would not be freed. Mr. Meshal said that the total would be 1,027, among them 315 prisoners serving life sentences and 27 women.

According to Israeli television, Israel would first release 450 prisoners as Sergeant Shalit is sent to Egypt, possibly in a week. Two months later, the television said, the remaining prisoners would be released. None of the details could be confirmed officially.

Sergeant Shalit was seized in a cross-border raid by Hamas and other Palestinian militant groups in June 2006 and taken into the Gaza Strip.

Hamas, which rejects Israel’s existence, is regarded by much of the West as a terrorist organization. It won Palestinian parliamentary elections in 2006 and took full control of Gaza in 2007, routing the Palestinian Authority forces loyal to President Abbas of Fatah, Hamas’s rival. Since then, Israel has maintained a blockade on Gaza to isolate Hamas, although it has eased many restrictions on imports.

A prisoner exchange deal for Sergeant Shalit had seemed close in late 2009, but the talks collapsed. Israel and Hamas each blamed the other. Israel had balked at releasing some of the prisoners demanded by Hamas, including those convicted as planners and perpetrators of some of the deadliest terrorist attacks in recent years.

Another stumbling block was Israel’s fear of letting some of the prisoners back into the West Bank where they might engage again in violence. Previous intelligence chiefs lobbied strongly against such a move.

But the chiefs of all three Israeli intelligence agencies — Mossad, Shin Bet and Military Intelligence — have been replaced in the past year and those objections were partly overcome, according to Israeli officials and analysts. In the current deal, only some prisoners were expected to be permitted into the West Bank.

Amnon Zichroni, an Israeli lawyer who has worked on such issues, told Israel Radio that one reason for the shift was that violence was a less popular form of protest against Israel in the West Bank today, and, he said, “there are increasing efforts to minimize any form of terrorism as a form of resistance.”

Despite efforts to renew peace talks between Israel and the Palestinian Authority, there is little optimism regarding success. The prisoner exchange, assuming it is carried out, seems likely to increase the popularity of Hamas among Palestinians as well as that of Mr. Netanyahu’s Likud Party in Israel, perhaps temporarily sidelining Mr. Abbas.

For years, Israelis have embraced the Shalit family, with many viewing the abducted soldier as, in effect, their own son.

Tens of thousands of Israelis joined the Shalits in the summer of 2010 for parts of a 12-day march from the Shalits’ home in northern Israel to Jerusalem to publicize their son’s plight. Since then, the parents have spent many days in a tent near the prime minister’s residence to draw attention to their son.

Mr. Netanyahu said he had telephoned the Shalits earlier in the day to tell them he was bringing their son home.

“When I took office I took it upon myself, as a personal mission, to bring Gilad home to his family,” Mr. Netanyahu said.

He said he had told his negotiators to hold the talks “under the guidelines important to Israel: the need to bring Gilad home and the need to keep Israel’s citizens safe.”

For Palestinians, the plight of thousands of their sons in Israeli prisons has been equally traumatic, and the possibility of their release drew enormous attention.

In Gaza, night had fallen when the news of a possible exchange began to circulate. Usama Sarhan, 34, a night security guard in a grocery store in Gaza City, expressed guarded optimism as he headed off to catch Mr. Meshal’s address on television. Wary because a deal had been reported to be close previously, he said that if the prisoner trade succeeded, it would be “a victory for Gaza.”

Later, thousands poured into the streets in Gaza and the West Bank in celebration.

Ismail Haniya, the top Hamas leader in Gaza, said at a public rally outside the parliament building in Gaza City that Hamas would begin preparations to receive the prisoners, but gave no indication of timing.

Among those celebrating on the streets was Bahaa al-Madhoun, a Hamas official, whose family was waving a Palestinian flag from their car as he drove past honking motorcycles and trucks blaring music.

“This is a huge happiness for the Palestinian people, that their prisoners are being released from prisons,” he said. “The Palestinian people have been waiting for that for years. The resistance won, and the Palestinian people won.”

In Israel, there were some mixed emotions.

Yehudit Shahor, whose teenage son Uri was killed by Palestinians in 1995, told Israeli television that “despite the fear I feel as an Israeli citizen and a terror victim, I am very happy for the Shalit family and feel moved as a mother that this boy will come home.”

But she said she had no doubt that any killers among the released Palestinians would kill again. She added: “I will never see Uri again, but Aviva Shalit has a chance to see her son Gilad. And even if this is a tough deal, a living boy must be returned home at all costs.”