The remaining Israeli hostages still held in the Palestinian territory will also be released as part of the agreement, which was struck following days of negotiations.
Keir Starmer said it was “the long-overdue news that the Israeli and Palestinian people have desperately been waiting for”.
Israel’s prime minister Benjamin Netanyahu said the deal had not yet been finalised, but could be within hours.
His office said Hamas had “caved in at the last minute”, paving the way for a ceasefire agreement to end the 15-month long conflict.
The war was triggered by the deadly attack on Israeli civilians by Hamas militants on October 7, 2023.
Donald Trump quickly tried to claim credit for the breakthrough, which comes just days before his inauguration as US president.
He said: “This EPIC ceasefire agreement could have only happened as a result of our Historic Victory in November, as it signalled to the entire World that my Administration would seek Peace and negotiate deals to ensure the safety of all Americans, and our Allies. I am thrilled American and Israeli hostages will be returning home to be reunited with their families and loved ones.
“With this deal in place, my National Security team, through the efforts of Special Envoy to the Middle East, Steve Witkoff, will continue to work closely with Israel and our Allies to make sure Gaza NEVER again becomes a terrorist safe haven.
“We will continue promoting PEACE THROUGH STRENGTH throughout the region, as we build upon the momentum of this ceasefire to further expand the Historic Abraham Accords. This is only the beginning of great things to come for America, and indeed, the World”
Starmer said: “After months of devastating bloodshed and countless lives lost, this is the long-overdue news that the Israeli and Palestinian people have desperately been waiting for.
“They have borne the brunt of this conflict – triggered by the brutal terrorists of Hamas, who committed the deadliest massacre of Jewish people since the Holocaust on October 7.
“The hostages, who were brutally ripped from their homes on that day and held captive in unimaginable conditions ever since, can now finally return to their families. But we should also use this moment to pay tribute to those who won’t make it home – including the British people who were murdered by Hamas. We will continue to mourn and remember them.
“For the innocent Palestinians whose homes turned into a warzone overnight and the many who have lost their lives, this ceasefire must allow for a huge surge in humanitarian aid, which is so desperately needed to end the suffering in Gaza.
“And then our attention must turn to how we secure a permanently better future for the Israeli and Palestinian people – grounded in a two-state solution that will guarantee security and stability for Israel, alongside a sovereign and viable Palestine state.
“The UK and its allies will continue to be at the forefront of these crucial efforts to break the cycle of violence and secure long-term peace in the Middle East.”
Lib Dem leader Ed Davey said: “The announcement of a ceasefire is, at last, a moment of hope after many months of darkness and despair for the region.
“As this ceasefire comes into effect, Palestinians will hope that the killing will now stop. Israeli hostages will finally be returned to their loved ones again after being held in captivity for fifteen months. The work of flooding Gaza with the aid which it has desperately needed for months must begin in earnest.
“Now, it is incumbent on the UK and the entire international community to do all it can to ensure that this ceasefire does not turn out to be a temporary truce. Otherwise we will not be able to get the remaining hostages home and finally alleviate the humanitarian crisis in Gaza.
“We must look back on this moment as the first step on the road to a lasting peace. That two-state solution - with a recognised Palestinian state based on 1967 borders - is the only way to deliver the dignity and security which Israelis and Palestinians deserve.”
Helen McEachern, chief executive of Care International UK, said it was “just the first step in stemming the overwhelming tide of suffering.”
She said: “A ceasefire will offer respite from the relentless bombardment imposed by Israeli authorities, and every effort must now be made to ensure it is sustained and made permanent.”