"This is the first time I'll be going to vote in any election, and it's definitely a big deal. My family has been talking about it for weeks," said Ibrahim Farrag Hassan, 64, who sells toys in a small market in central Cairo.
Around 50 million eligible voters are being called to choose Mubarak's successor on Wednesday and Thursday with a run-off scheduled for next month should there be no outright winner.
"This election will change things, whoever is coming will be scared of the people and will have to listen to them," said Hind Ahmed, 25, a shop assistant at a lingerie store.
"All my friends and family are talking about the elections all the time. It's the first time in their lives that any of them are voting in a presidential election because this time the result isn't known in advance."
Campaigning for the landmark poll ended on Sunday night, with candidates banned from giving any media interviews or making public appearances for 48 hours before the election.
But the campaign silence did little to dim the excitement in the capital.
"Tomorrow is the big exam, I have knots in my stomach and can't sleep," giggled Warda, 25, an attendant in an upmarket sports club.
After decades of pre-determined results, for the first time, the outcome of the vote -- which pits Islamists against secularists and revolutionaries against old regime members -- is wide open.
The main contenders are former foreign minister and Arab League chief Amr Mussa; Ahmed Shafiq, the last premier to serve under Mubarak; the Muslim Brotherhood's Mohammed Mursi; independent Islamist Abdel Moneim Abul Fotouh and Nasserist candidate Hamdeen Sabbahi.
Prime Minister Kamal al-Ganzuri on Tuesday urged for calm during the election and urged political forces to accept the results of the historic vote, echoing a call a day earlier by the ruling military.
Ganzuri asked Egyptians to "stand together to ensure the success of the electoral process and to accept the decision of the majority of Egyptians who will express their will through the ballot boxes."
In a statement, he expressed hope that the elections proceed with calm and called on candidates, political forces, parties to urge their supporters to respect the will of others and accept the results of the election.
In the city an army vehicle rumbled through Tahrir Square -- the epicentre of protests that toppled Mubarak -- urging Egyptians to vote.
"Rise, Egyptian; Egypt is calling you," the soldier shouted through a loudspeaker, borrowing the lyrics from a popular nationalist song by iconic composer Sayyed Darwish.
"It's the first time your vote will count, don't stay at home," he pleaded.
On Monday, the Supreme Council of the Armed Forces, which took power when Mubarak was deposed, called on Egyptians to accept the results of the looming election.
In a statement posted on its Facebook page, the SCAF stressed the importance of accepting the results of the election which will reflect the choice of the free Egyptian people.