The legislation repeals the 1972 Bill which brought Britain into the European Economic Community and translates all EU rules into British laws.
According to various reports, Juncker is due to lay out a roadmap for the "renaissance" of the European Union once Britain leaves the bloc.
Previously referred to as the Great Repeal Bill, the EU Withdrawal Bill overturns the 1972 European Communities Act which took the United Kingdom into the then European Economic Community.
It was the second crucial parliamentary victory for the government in two days after the EU (Withdrawal) Bill, which will bring EU law onto the United Kingdom statute books post-Brexit, passed with a majority of 36 in the early hours of Tuesday morning.
The government has promised concerned lawmakers that ministers would not use the wide-ranging powers to make "substantive changes" to law and some have said they will seek changes to the bill at later stages.
It is controversial because it hands sweeping powers to ministers to change legislation as they see fit, without full scrutiny in Parliament.
Despite attempts from Labour, the Liberal Democrats and Scottish National Party to band together in opposition to the bill, the post-midnight vote was a comfortable victory for May.
"This bill is an affront to parliamentary democracy and a naked power grab by government ministers".
"Labour will seek to amend and remove the worst aspects from the bill but the flaws are so fundamental it's hard to see how this could ever be made fit for goal", the Labour MP said.
"This is a dark day for the mother of parliaments", he said.
Slow progress in Brexit talks, however, has stirred fears of a messy breakup that could leave British businesses with little legal clarity on emissions.
The Government is also offering to agree joint foreign policy positions with Brussels, including co-operating on global sanctions against states or terrorist organisations.
"It's in our mutual interest to work closely with the European Union and its member states to challenge terrorism and extremism, illegal migration, cyber-crime, and conventional state-based military aggression".
"A vote against this bill is a vote for a chaotic exit from the European Union", Davis said in a statement.
Verhofstadt said lawmakers are set to debate on October 3 whether the negotiations should be broadened to discuss trade and the shape of post-Brexit relations.