A source familiar with the matter said Alexander would likely be released on Tuesday.
The announcement on Sunday night comes shortly before US President Donald Trump visits the Middle East this week.
Trump is not planning to visit Israel.
Alexander is an Israeli-American soldier who grew up in the United States.
He was abducted from his base during the October 7, 2023, Hamas-led attack that ignited the war in Gaza.
Meanwhile, Israeli strikes killed 15 people in the Gaza Strip, mostly women and children, according to local health officials.
Two of the weekend strikes hit tents in the southern city of Khan Younis, each killing two children and their parents, according to Nasser Hospital, which received the bodies.
Another seven people were killed in strikes elsewhere, including a man and his child in a Gaza City neighbourhood, according to hospitals and Gaza's Health Ministry.
The Israeli military says it only targets militants and tries to avoid harming civilians.
It blames Hamas for civilian deaths in the 19-month-old war because the militants are embedded in densely populated areas.
There was no immediate Israeli comment on the latest strikes.
Israel has sealed Gaza off from all imports, including food, medicine and emergency shelter, for over 10 weeks in what it says is a pressure tactic aimed at forcing Hamas to release hostages.
Israel resumed its offensive in March, shattering a ceasefire that had facilitated the release of more than 30 hostages.
The UN and aid groups say food and other supplies are running low and hunger is widespread.
Children carrying empty bottles raced after a water tanker in a devastated area of northern Gaza on Sunday.
Residents of the built-up Shati refugee camp said the water was brought by a charity from elsewhere in Gaza.
Without it, they rely on wells that are salty and often polluted.
"I am forced to drink salty water, I have no choice," said Mahmoud Radwan.
"This causes intestinal disease, and there's no medicine to treat it."
COGAT, the Israeli military body in charge of Palestinian civilian affairs, says enough aid entered during a two-month ceasefire this year and that two of the three main water lines from Israel are still functioning.
Aid groups say the humanitarian crisis is worse than at any time in the 19-month war.
US President Donald Trump, whose administration has voiced full support for Israel's actions, is set to visit Saudi Arabia, Qatar and the United Arab Emirates this week in a regional tour that will not include Israel.
Talks between Hamas and the US administration regarding a ceasefire in Gaza and the entry of humanitarian aid to the besieged enclave were underway, a senior Palestinian official familiar with the discussions told Reuters on Sunday.
The war began when Hamas-led militants attacked southern Israel on October 7, 2023, killing some 1200 people, mostly civilians, and taking 251 hostage.
Fifty-nine hostages are still inside Gaza, around a third of them believed to be alive, after most of the rest were released in ceasefire agreements or other deals.
Israel's offensive has killed over 52,800 Palestinians, mostly women and children, according to Gaza's Health Ministry, which does not say how many of the dead were combatants or civilians.
The offensive has destroyed vast areas of the territory and displaced some 90 per cent of its population of around two million.
with Reuters
