"The US President-elect Donald Trump expressed his utmost appreciation to the president, pointing out that his was the first international call he had received to congratulate him on winning the election," the presidency said in a statement.
"Trump said he looked forward to meeting the president (again) soon."
Sisi, who had met with Trump during his visit to New York to attend UN General Assembly in September, said he hoped the business tycoon's election would help breathe new life into US-Egyptian ties.
He also extended an invitation for Trump to visit Cairo once he takes office.
Trump won the US Presidential elections on Tuesday in what has been described as potentially one of the biggest upsets in US Presidential election history.
'Setback for Islamists'
Despite Trump's anti-Muslim rhetoric, many Egyptians welcomed his victory, arguing it could be a positive development for Egypt.
Speaking to parliamentary reporters on Wednesday, several Egyptian MPs said Trump's victory meant a major setback for the Muslim Brotherhood group - banned in Egypt - and other Islamist movements.
"Trump's victory represents a radical departure from the Obama-Clinton clan who supported the Muslim Brotherhood and other political Islam movements," Coptic MP Margaret Azer said in a statement.
"In fact, Hilary Clinton was the candidate of the Muslim Brotherhood - rather than the Democratic party - in the US presidential election," she added.
Clinton, who served as the US Secretary of State during the 2011 Arab Spring uprisings, is unpopular among many Egyptians, who saw her as a long-standing supporter of toppled dictator Hosni Mubarak.
However, Sisi supporters consider Clinton too sympathetic with the Muslim Brotherhood, which was banned after Islamist President Mohamed Morsi was toppled by a military coup in 2013.
|The US President-elect Donald Trump expressed his utmost appreciation to the president, pointing out that his was the first international call he had received to congratulate him on winning the election
- Presidency statement
"The election of Trump should also help put an end to the terrorist group ISIS and to chaos in Syria," she said, referring to the Islamic State militant group that took over swathes of Syria and Iraq in 2014.
Azer hopes Trump will move quickly to restore old strategic relations between Egypt and the United States.
"This strategic relationship is necessary for America to win the fight against terrorism in the Middle East," she said.
The Egyptian Parliament's Human Rights Committee also issued a statement on Wednesday, saying that Trump's election should not come as a surprise.
The committee's chairperson Alaa Abed accused Obama and Clinton of spending billions of dollars to support Islamist movements in the Middle East.
"They were under false convictions that these movements are moderate and democratic, and in this way they gave them cover to spread their terrorism and poisonous ideology in the Middle East," he said.
"If [Trump] is really serious about fighting radical Islam, he should win big allies like Egypt."
In one of his foreign policy speeches last summer, Trump said he would call for an international conference on terrorism, with King Abdallah of Jordan and President Sisi of Egypt on top of the list of invitees.
Egypt receives an annual $1.3 billion worth of military aid from the United States.