At the entrance to West Jerusalem's famous Mahane Yahuda market, a keen Donald Trump fan is still celebrating.

"Go Trump, Go Trump!" yells a man in a Trump T-shirt, dancing and waving the American and Jerusalem flags.

Key points: President-elect Donald Trump has claimed he will be the most "pro Israel president ever"

President-elect Donald Trump has claimed he will be the most "pro Israel president ever" Mr Trump has said he will recognise Jerusalem as Israel's capital, and move the American embassy from Tel Aviv

Mr Trump has said he will recognise Jerusalem as Israel's capital, and move the American embassy from Tel Aviv Mr Trump also signalled he may end longstanding White House opposition to increased Israeli settlement in the Palestinian West Bank

"They were, laughing at him saying he's crazy," the man, who would not give his name, told the ABC.

"But in the end he showed them!"

On the Israeli side of Jerusalem, many are welcoming Mr Trump's election, saying they feel the President-elect is firmly on "their side".

"I think he understands what situation we are in. Surrounded by a lot of problems and enemies," 42-year-old shopper Betty said.

"So I think he will be good for Israel, at least according to his promises."

Mr Trump's promises to the Israelis have been vast; starting with the claim he will be the most "pro Israel president ever".

"I think if there is any issue on which Trump has actually made his views clear it is Israel. That he intends to be extremely pro Israel," said Gil Hoffman, chief political correspondent for the Jerusalem Post newspaper.

Gil Hoffman is the chief political correspondent for the Jerusalem Post newspaper. ( ABC News: Sophie McNeill )

"Really good times are ahead for [Prime Minister Benjamin] Netanyahu and for Israel in general.

"It's like John Howard became the leader of the free world!"

Mr Trump has said he would recognise Jerusalem as Israel's capital and move the American embassy from Tel Aviv to the disputed city, something former president George Bush promised but never delivered.

Mr Trump also said he would "tear up" the multi-lateral Iran deal, a move that would be greatly welcomed by the Israeli Government but extremely difficult to execute in reality.

Palestinian leadership waiting to see policies

Despite the challenges of executing such promises, many Israelis are still excited; particularly after Mr Trump signalled he may end longstanding White House opposition to increased Israeli settlement building in the Palestinian West bank.

"Understand Israel has been through a presidency of Barack Obama who acted like a schoolmarm, vigorously enforcing his rules about not one brick being built anywhere over Israel's pre '67 borders," Mr Hoffman said.

An Israeli soldier patrols in the occupied West Bank town of Bethlehem on Friday. ( ABC News: Sophie McNeill )

"And here we are getting rid of him and replacing him with a new teacher who will basically let Israel do what ever it wants."

Xavier Abu Eid, an advisor to the Palestine Liberation Organization Negotiation Affairs Department, said the Palestinian leadership was waiting to see what a Trump presidency looked like before they decided to panic.

"We deal with polices, not personalities," Mr Abu Eid said.

"We think it's too early to cry or to make a party out of Mr Trump's election."

But on the streets of Palestinian East Jerusalem, people have already started to worry.

Abed said the Palestinians had "lost hope". ( ABC News: Sophie McNeill )

"There is no room to build a Palestinian state, from the north to the south — where are we going to build this Palestinian state?" 62-year-old Abed asked.

Abed said the Palestinians had so much hope in President Obama's presidency but eight years later, they feel worse off than ever.

"We lost hope," said Abed.

"Everyone makes promises from one election to the next but each president just puts the responsibility on the next president. And we witness that with each election nothing at all is achieved."

Mr Netanyahu has already been invited to visit Mr Trump once when he moves into the White House in January.

Both Israelis and Palestinians will be watching closely to see where it goes from there.