The hostages were expected be reunited with their families on Monday and undergo medical checks in Israel.
Seven have already arrived in Israel, while another 13 were handed to Red Cross officials, who began transporting them through Gaza, the Israeli military said.
As well as the 20 living hostages expected to be released, more than 1900 Palestinian prisoners held by Israel are set to be freed.
The bodies of the remaining 28 dead hostages are also expected to be handed over as part of the deal, although the exact timing remained unclear.
Families and friends of hostages broke out into wild cheers as Israeli television channels announced the hostages were in the hands of the Red Cross.
Tens of thousands of Israelis were watching the transfers at public screenings across the country, with a major event being held in Tel Aviv.
Buses carrying freed Palestinian detainees as part of the ceasefire and hostage release deal also began moving towards the Palestinian enclave from Israeli prisons, footage on Israeli television showed.
"This is a great day. This is a new beginning," US President Donald Trump said after arriving to a hero's welcome in Israel where he was addressing parliament before flying on to Egypt for a summit aimed at building conditions for a lasting peace in Gaza.
Asked if the two-year Gaza war was over, he said: "Yes."
A surge of humanitarian aid was expected into famine-stricken Gaza, where hundreds of thousands of people have been left homeless.
While major questions remain about the future of Hamas and Gaza, the exchange of hostages and prisoners marked a key step towards ending the deadliest war ever between Israel and the militant group.
The hostages' return caps a painful chapter for Israel.
Since they were captured in the October 2023 Hamas attack that ignited the war, newscasts have marked their days in captivity and Israelis have worn yellow pins and ribbons in solidarity.
Tens of thousands have joined their families in weekly demonstrations calling for their release.
As the war dragged on, demonstrators accused Prime Minister Benjamin Netanyahu of dragging his feet for political purposes, even as he accused Hamas of intransigence.
Last week, under heavy international pressure and increasing isolation for Israel, the bitter enemies agreed to the ceasefire.
The living hostages were handed to the International Committee of the Red Cross and then to the Israeli military, which will take them to the Reim military base to be reunited with families.
The released Palestinian prisoners include 250 people serving life sentences for convictions in attacks on Israelis, as well as 1700 seized from Gaza during the war and held without charge.
Trump will continue to Egypt, where President Abdel Fattah el-Sissi's office said he would co-chair a "peace summit" on Monday with regional and international leaders, including Mahmoud Abbas, leader of the internationally recognised Palestinian Authority.
Netanyahu has rejected any role in postwar Gaza for Abbas, though the US plan leaves the possibility open if his Palestinian Authority undergoes reforms.
Hamas seized control of Gaza in 2007.
Other key questions in the ceasefire deal have yet to be resolved, including the future governance of Gaza and who will pay for a billion-dollar reconstruction process.
Israel wants to ensure the weakened Hamas disarms, and Netanyahu has warned Israel could do it "the hard way".
Hamas refuses to disarm and wants to ensure Israel pulls its troops completely out of Gaza.
The Israeli military has withdrawn from much of Gaza City, the southern city of Khan Younis and other areas.
The United Nations says Israel has approved 190,000 tonnes of aid to enter Gaza, which was besieged after Israel ended the previous ceasefire in March.
The war began when Hamas-led militants launched a surprise attack on southern Israel on October 7, 2023, in which some 1200 people were killed and 250 taken hostage.
In Israel's ensuing offensive, more than 67,000 Palestinians have been killed, according to Gaza's health ministry.
