The decision to reopen the compound, also holy to Jews who call it the Temple Mount, was taken by Prime Minister Benjamin Netanyahu who was leaving for an official visit to France.
"It has been decided to reopen the Temple Mount gradually tomorrow (Sunday) for the faithful, visitors and tourists," the premier's office said in a statement.
Three Arab Israeli assailants opened fire on Israeli police on Friday in the Old City before fleeing to the nearby Haram al-Sharif compound -- Islam's third holiest site -- where they were shot dead by police.
Israeli authorities said they had come from the flashpoint holy site, which includes the Al-Aqsa mosque and the Dome of the Rock, to commit the attack.
The White House "strongly" condemned Friday's attack, saying "there must be zero tolerance for terrorism".
After the attack Israeli authorities took the highly unusual decision to close the holy site for Friday prayers, angering Muslims and drawing the ire of Jordan which administers the compound.
Wael Arabiyat, Jordan's Islamic affairs minister, warned that keeping Al-Aqsa mosque closed is "dangerous" and "unprecedented", after Amman called for its immediate reopening.
Hundreds of Jordanians, responding to a Muslim Brotherhood call, demonstrated in Amman on Saturday, calling for the "liberation of Al-Aqsa".
Netanyahu had said the compound could reopen Sunday after security was assessed, and rejected Jordan's criticism.
On Saturday, Israeli security forces locked down parts of Jerusalem's Old City, restricting access through Damascus Gate, the main entrance used by Palestinians.
Only residents with identification were allowed to pass.
"This is not security. This is punishment," said Bader Jweihan, 53, an accountant who was denied entry.
City for all
Musa Abdelmenam Qussam, 73 and with poor eyesight, was helped by a grandson as he walked with a cane and sought to enter.
But the owner of a book wholesale shop in the Old City was also turned away.
"This mosque is not only for Muslims. Tourists come," he said, adding that he usually prays at Al-Aqsa every day.
"This city is for all the world. It must be open."
Jaffa Gate, heavily used by tourists and near the Old City's Jewish Quarter, was open but with a heavy police presence.
A group of tourists from Poland said they were concerned when they heard about Friday's shooting but wanted to continue their visit.
"It stressed me a little," said Ewa, who did not want to give her last name.
At Lions Gate near the site of the attack, police guarded the entrance and restricted access, checking IDs.
The attack and aftermath was one of the most serious incidents in Jerusalem in recent years.
Palestinian president Mahmud Abbas and Netanyahu spoke by phone on Friday as tensions rose.
Israeli authorities also detained Jerusalem's top Muslim cleric, grand mufti Muhammad Ahmad Hussein, as crowds gathered at the gates of the Old City after the attack, his son said.
Hussein was released later Friday after being questioned, another of his sons said.
'Worst aggression'
With Al-Aqsa closed, crowds gathered at Old City gates and held Friday prayers there instead.
The Palestinian director of the Waqf (religious property) council, Abdel Azim Salhab, said the closure of the mosque compound was the "worst aggression since 1967".
He was referring to the start of Israel's occupation of east Jerusalem, which it later annexed in a move never recognised by the international community.
The Haram al-Sharif/Temple Mount is central to the Israeli-Palestinian conflict, with Palestinians fearing Israel may one day seek to assert further control over it.
Jews who also consider it their most sacred site are allowed to visit but not pray there to avoid provoking tensions.
Netanyahu's office said security would be increased with metal detectors at the entrances to the site and security cameras outside it.
A wave of unrest that broke out in October 2015 has claimed the lives of at least 281 Palestinians or Arab Israelis, 44 Israelis, two Americans, two Jordanians, an Eritrean, a Sudanese and a Briton, according to an AFP toll.
Israeli authorities say most of the Palestinians killed were carrying out knife, gun or car-ramming attacks.
Others were shot dead in protests and clashes, while some were killed in Israeli air strikes on the Gaza Strip.
The violence had greatly subsided in recent months.
