The U.S. move fulfilled a pledge by President Donald Trump, who has recognised the holy city as the Israeli capital, but it has fired Palestinian anger and drawn criticism from many foreign governments as a set back to peace efforts.
At the embassy inauguration ceremony, Israeli Prime Minister Benjamin Netanyahu thanked Trump for "having the courage to keep your promises".
"What a glorious day for Israel," Netanyahu said in a speech. "We are in Jerusalem and we are here to stay."
Trump, in a recorded message, said he remained committed to peace between Israel and the Palestinians.
On the Gaza border, Palestinian protests quickly turned into bloodshed.
Israeli gunfire killed at least 52 Palestinians, the highest toll in a single day since a series of protests demanding the right to return to ancestral homes in Israel began on March 30.
Palestinian Health Ministry spokesman Ashraf Al-Qidra said the dead included six children under the age of 18. About 2,400 Palestinians had been wounded, about half of them by live bullets.
France called on Israel to show restraint and U.N. Secretary-General Antonio Guterres said he was "deeply concerned" by the events in Gaza.
Tens of thousands of Palestinians had streamed to the coastal enclave's land border, some approaching the Israeli fence - a line Israeli leaders said Palestinians would not be allowed to breach. Clouds of black smoke from tyres set alight by demonstrators rose in the air.
Demonstrators, some armed with slingshots, hurled stones at the Israeli security forces, who fired volleys of tear gas and intense rounds of gunfire.
"Today is the big day when we will cross the fence and tell Israel and the world we will not accept being occupied forever," said Gaza science teacher Ali, who declined to give his last name.
Trump's recognition of contested Jerusalem as Israel's capital in December outraged Palestinians, who said the United States could no longer serve as an honest broker in any peace process with Israel.
Palestinians seek East Jerusalem as the capital of a state they want to establish in the occupied West Bank and the Gaza Strip.
Israel regards all of the city, including the eastern sector it captured in the 1967 Middle East war and annexed, as its "eternal and indivisible capital" in a move that has not won international recognition.
Most countries say the status of Jerusalem - a sacred city to Jews, Muslims and Christians - should be determined in a final peace settlement and that moving their embassies now would prejudge any such deal. Peace talks aimed a finding a two-state solution to the conflict have been frozen since 2014.
WHEELCHAIR PROTESTER
The Palestinian dead on Monday included a medic and a man in a wheelchair who had been pictured on social media using a slingshot.
The Israeli military said three of those killed were armed militants whom it said tried to place explosives near the fence in the southern Gaza Strip.
The latest casualties raised the Palestinian death toll to 88 since the protests started six weeks ago, the worst bout of bloodshed since the 2014 Gaza war. No Israeli casualties have been reported.
At the protest sites, families sat in the shade of tents nearly 800 metres (yards) from the border fence. Hundreds of protesters ventured closer to the barrier, rolling burning tyres and hurling stones.
Some flew flaming kites to try and torch bushes on the other side and distract Israeli marksmen. Hundreds of Palestinians were treated for tear gas inhalation.
"The IDF (Israel Defence Forces) will act forcefully against any terrorist activity and will operate to prevent attacks against Israelis," the military said in a statement.
The killings have drawn international criticism in recent weeks, but the United States has echoed Israel in accusing Gaza's ruling Hamas movement of instigating violence, an allegation it denies.
More than 2 million people are crammed into the narrow strip, which is blockaded by Egypt and Israel
TRUMP PEACE PLAN
The Trump administration has nearly completed a long-awaited Israeli-Palestinian peace plan but is undecided on how and when to roll it out, given Palestinians' outrage over the embassy move and their contention that Washington can no longer be an honest broker.
Palestinian Prime Minister Rami Hamdallah, in a statement on Monday, accused the United States of "blatant violations of international law".
The protests are scheduled to culminate on Tuesday, the day Palestinians mourn as the "Nakba" or "Catastrophe" when, in 1948, hundreds of thousands of them were driven out of their homes or fled the fighting around Israel's creation.
"Choosing a tragic day in Palestinian history (to open the Jerusalem embassy) shows great insensibility and disrespect for the core principles of the peace process," Hamdallah wrote.
In London, the British government said it had no plans to move its Israel embassy from Tel Aviv to Jerusalem, and said it disagreed with the U.S. decision to do so.
The Russian government said it feared the embassy move would increase tensions across the Middle East.
French Foreign Minister Jean-Yves Le Drian said the U.S. move flouted international law.
"France calls on all actors to show responsibility to prevent a new escalation," Le Drian said in a statement.
The U.N.'s Guterres, speaking to reporters in Vienna, said
the Gaza blooshed showed the need for a political solution. "There is no Plan B to a two-state solution in which Israelis and Palestinians can live in peace," he said.
The Afghan Taliban, in a rare comment on matters outside Afghanistan, condemned the U.S. Embassy move and called on Muslim countries to oppose it.
