The two former prime ministers were both jailed on corruption charges by the caretaker regime but then released in order to contest the elections.
Sohail Rahman, Al Jazeera's correspondent reporting from Dhaka, the capital, said: "These two women are, at present, completely innocent.
"The charges against them are still there. They are on bail and they are pending, but there has been no court case, and legally if they do win the election either of them can become prime minister."
Some 50,000 troops have been deployed and 600,000 police officers will man polling booths in a bid to eliminate election fraud and threatened attacks by religious armed groups.
The winner of Monday's election, either a single party or a coalition of parties, needs 151 of the 300 seats in the National Assembly.
History of coups
For the first time, voters have the choice of casting a "no" vote by ticking a "none of the above" box on their ballot papers.
Commentators say Monday's polls will be the fairest in the country after the current regime created a digital electoral roll eliminating 12.7 million fake "ghost" voters.
There are some 200,000 electoral observers, including 2,500 from abroad.
Bangladesh has a long history of coups and counter-coups since winning independence from Pakistan in 1971.
The Awami League and the BNP have often been accused of anti-democratic tactics, with both regularly boycotting parliament and staging national strikes when in opposition.
Bangladesh's current regime has been in power since January 2007 when the army stepped in, imposed a state of emergency and cancelled elections after months of political violence killed at least 35 people.
A short but vigorous election campaign has been under way since December 12.