At the same time, Israel was sending buses carrying hundreds of Palestinians prisoners into Egypt on their way to Gaza, where they will be greeted by a massive celebration.
"Until we see him, we are following with concern and anticipation," said Sgt. Gilad Schalit's father, Noam, speaking on Israel Radio from an air base inside Israel where his family was waiting to reunite with him.
The deal, the most lopsided prisoner swap in Israeli history, caps a five-and-a-half-year saga that has seen multiple Israeli military offensives in Gaza, an Israeli blockade on the territory and numerous rounds of failed negotiations.
The swap got under way early Tuesday as Hamas moved Sgt. Gilad Schalit across Gaza's border with Egypt, while Israel simultaneously began freeing the Palestinian prisoners. At midmorning, Mahmoud Zahar, a Hamas leader in Gaza, said his group was no longer holding the soldier.
Hamas' Al-Aqsa TV reported that a high-level Hamas delegation arrived on the Egyptian side to hand over Schalit and to greet the returning prisoners.
Asked in a brief TV appearance whether this was the happiest day of his life, Noam Schalit said: "Yes, you can make that assumption." Noam Schalit has become a ubiquitous figure in Israel since his son's capture and led a massive campaign to press the government into bringing the 25-year-old home.
Before dawn, convoys of white vans and trucks transported hundreds of Palestinian prisoners to the locations in the West Bank and on the Israel-Egypt border where they were to be freed.
Preparations for a mass rally to greet the prisoners were in high gear in a large field in Gaza City. Hamas organizers set up neat rows of thousands of plastic chairs and erected a large stage that can hold hundreds of people. The stage was decorated with a huge mural depicting the capture of Schalit. Hamas orderlies handed out sandwiches and soft drinks to people arriving.
Armed Hamas security guards were deployed on rooftops overlooking the field.
In the West Bank, located on the opposite side of Israel, about 200 relatives of prisoners waited at a West Bank checkpoint as the exchange unfolded.
"We're so excited we can barely breathe," said Mariam Shkair, waiting for her brother, 52-year-old Abdel Latif, who spent 25 years in prison for killing an Israeli soldier. "We are waiting to hug him."
Some of the relatives raised Palestinian flags or the green banners of Hamas. A group of young men chanted, "We will continue our struggle."
The exchange, negotiated through Egyptian mediators because Israel and Hamas will not talk directly to each other, is going ahead despite criticism and court appeals in Israel against the release of the prisoners. Nearly 300 of them were serving lengthy sentences for involvement in deadly attacks.
The exchange involves a delicate series of staged releases, each one triggering the next. The Red Cross and Egyptian officials are involved in facilitating the movement of prisoners.
In Gaza, Hamas militants deployed in force along the road leading into Egypt where Schalit was taken. Shortly thereafter, hundreds of returning Palestinians were slated to enter Gaza on the same road.
When Tuesday's exchange is complete, 477 Palestinians held in Israeli jails, including 27 women, will have been released, several of them after decades behind bars.
More than 200 prisoners, originally from the West Bank, will instead be sent to the fenced-off Gaza Strip. And some 40 prisoners will be deported to Syria, Qatar, Turkey and Jordan, Palestinian officials said. Another 550 prisoners are slated to be released in two months.
Israel's Channel 10 TV said there was a delay at midmorning because two women were refusing to be sent to Gaza and instead asking to be sent to Egypt.
Little is known about Schalit's condition. Although he appeared healthy in the only time he has been seen in captivity -- in a brief and scripted 2009 video released by Hamas -- he was denied all visits, including by the Red Cross, and the state of his mental and physical health is unclear.
Schalit will then be flown by helicopter to an air force base in central Israel, where he will meet his parents, as well as Prime Minister Benjamin Netanyahu, the defense minister and military chief of staff.
An intense media campaign to free Schalit made him a national symbol in Israel, and all local radio and TV stations held special live broadcasts Tuesday, following every step of the exchange.
Israel and Hamas have held numerous rounds of talks through German and Egyptian mediators. But officials on both sides have said that conditions prompted in part by the recent Egyptian revolution helped drive them to an agreement. Both sides have been eager to have good ties with the new Egyptian leadership, which brokered the deal.