The House of Commons Speaker insisted it would not be an "earth-shattering change" if elections were conducted with such technology in future.
He also suggested that MPs could be allowed to vote electronically in Parliament, after centuries in which they have been manually counted through division lobbies.
In a speech to the Policy Exchange think tank in London, Mr Bercow said the Commission on Digital Democracy which he set up at the start of the year would publish its findings in 2015.
"I know some do believe that voting ought to have an element of difficulty," Mr Bercow said. "The argument is that a good citizen should have to make an effort to vote, picking up a postcard posted to them weeks before and dragging themselves down to an empty community hall or primary school on a wet Thursday, to put a cross on a tiny piece of paper.
"Sorry, but I am not convinced this is the pinnacle of 21st century democracy in action. Yes, of course there are well-rehearsed arguments regarding electronic and internet voting and the integrity of the ballot box must be absolutely protected.
"That said, in an era in which many people bank, search for a partner and conduct their most private business online, treating their mobile phone or tablet as an extension of themselves, why should we not enable them to register to vote, cast their vote or express their views on the issues of the day using the same or similar tools?"