They will be the first such elections since the previous chamber was dissolved by a court ruling in 2012.
The authorities say the poll is the final step in a transition to democracy.
However, critics say most candidates are supporters of President Abdul Fattah al-Sisi and the new parliament is likely to strengthen his control.
Polling stations are expected to open at 08:00 local time (06:00 GMT) and close from 19:00.
The election consists of two rounds of voting and results are not expected to be known until early December.
Voters will choose 596 MPs for the lower house, the House of Representatives.
Security will be tight across the country with at least 185,000 troops supporting police, Egyptian news agency Mena reported.
Will Egypt's democracy be restored?
On Saturday, President Sisi made a televised appeal for Egyptians to vote.
"Line up in front of polling stations and plant with your votes the hope for a bright tomorrow for our new Egypt," he said.
President Sisi is a former general who led the 2013 military overthrow of Islamist President Mohammed Morsi, following months of unrest.
Mr Morsi's party, the Muslim Brotherhood, won about half the seats in the last parliament but is now banned and its leaders are in jail - some facing death sentences.
In contrast, many figures from the regime of deposed autocrat Hosni Mubarak are on the ballot paper, says the BBC's Orla Guerin in Cairo.
While the new parliament appears to have broad powers, it is not expected to challenge the president, she adds.
Analysts say turnout is expected to be low, with many Egyptians disillusioned with the democratic process.
Apathy is particularly high among young people, with many angry at the government and its policies.
Polls are due to open in Egypt in the first round of long-delayed elections to choose a new parliament.