His announcement comes after Theresa May said she will trigger Article 50 on March 29.
Mr Fallon is likely to face opposition within the chamber after a similar proposal included as part an amendment to the European Union (Notification of Withdrawal) Bill, was defeated last month by a majority of 307.
Tim Farron wants a second referendum over the terms of Brexit
Mr Fallon said: "The jeering and jingoism will no doubt be loud today in the Commons when I aim to give the people the final say on the Brexit deal – I would expect nothing less of Conservatives and, often, Labour MPs.
Mrs May has previously insisted that Parliament will get a vote on the final Brexit deal.
But Mr Fallon has vowed to fight for another two more years on a second referendum over Brexit.
Brexit: Results of how the UK voted Mon, March 20, 2017
Much of the North East of the United Kingdom voted to leave the European Union including Sunderland, Gateshead, Darlington, Durham, Hartlepool, Middlesbrough, Stockton, Redcar and Cleveland, North Tyneside and South Tyneside, and Northumberland
Getty Images 1 of 8
GREAT YARMOUTH: The town of Great Yarmouth on the East Coast of England voted by 72% to leave the European Union.
This is not about 'blocking Brexit'
The Lib Dem leader has denied his plan was about "blocking" Brexit.
Get Quotes on Home Insurance
He added: ”This is not about 'blocking Brexit', it's about holding Theresa May to account – such as for wanting to take Britain out of the world's largest market and customs union, even if there is no new trading arrangement in place.
"To question that is not disloyal.”
Mr Farron says his plans are not too block Brexit
Mr Fallon claims Brexit will hit living standards hard in the UK and that giving up on on the EU’s single market would be a mistake.
He continued: ”The disloyalty to the British people would be if I were bullied into silence, as Labour have been, and fail to warn how a hard Brexit will hit living standards and future generations."
Theresa May has announced she will trigger Brexit on March 29
Speaking earlier to the BBC, he said: “It’s foolish to think that somehow trade with New Zealand, Australia, or even the United States can match the enormous benefit of being in the single market.”
Mr Farron will have 10 minutes to make the case for introducing his Terms of Withdrawal From the European Union (Referendum) Bill to Parliament, with a further 10 minutes allowed for another MP to oppose it.
Another Terms of Withdrawal from EU (Referendum) Bill (HC Bill 26) sponsored by Labour MP Geraint Davies is expected to go before the House of Common for a second reading on Friday.