The EU (Withdrawal Agreement) Bill, which would implement the Brexit agreement Johnson had reached with the bloc in October, was introduced in Thursday's Queen's Speech, setting out the government's priorities for the next year, reports the BBC.
The Bill would also ban the government from extending the transition period, where the UK is out of the EU but follows many of its rules, past 2020.
On Friday, MPs will have their first chance to debate it in the House of Commons.
MPs have been given a further three days, January 7, 8 and 9, 2020, to continue their debate in the Commons.
With the Conservatives having won an 80-seat majority at the December 12 general election, the bill is expected to pass easily, before it moves on to further scrutiny by MPs and the House of Lords.
Ahead of Friday's debate, Johnson said: "We will deliver on the promise we made to the people and get the Brexit vote wrapped up for Christmas," the BBC reported.
An earlier withdrawal agreement - reached between former Prime Minister Theresa May and the EU - was rejected three times by MPs.
"After years of delay and rancour in Parliament, we will deliver certainty and hard-working businesses and people across this country will have a firm foundation on which to plan for the future.
"Next year will be a great year for our country - the year we get Brexit done, boost NHS funding, invest in infrastructure and level up access to opportunity and prosperity across our great nation," he added on Thursday.
In the 2016 referendum, the UK voted by 52 per cent to 48 per cent to leave the EU.
But the subsequent difficulties in getting Brexit through Parliament have caused gridlock at Westminster.
( With inputs from IANS )