The Prime Minister will take control of the Brexit negotations in a major snub to Mr Raab, who replaced David Davis earlier this month.
The Cabinet Office’s Europe Unit, which reports direct to the Prime Minister, will have “overall responsibility” for the exit talks, Mrs May said.
It is understood the Prime Minister wants to speed up Brexit negotiations in order to secure a favourable divorce deal with Brussels.
Mr Raab’s predecessor David Davis only held four hours of direct talks with EU negotiator Michel Barnier this year before his resignation.
Liberal Democrat MP Layla Moran and Remain supporter said: “It’s a demotion for Dominic Raab, we can all see that.
“The Prime Minister has shown how wafer-thin her confidence in the new Brexit Secretary is.”
Labour’s shadow Brexit Secretary Sir Kier Starmer tweeted: “That didn’t take long! Less than two weeks into the job…”
Shadow Brexit minister Jenny Chapman added: “Dominic Raab has been side-lined before he’s even had the chance to get his feet under the table.”
Follow our live blog below for the latest Brexit updates:
Brexit Secretary Dominic Raab has been ‘demoted’ by Theresa May
10:42pm: Gove optimistic over Brexit deal
Michael Gove has said the chances of the UK getting tariff-free access to European food markets after Brexit is “overwhelmingly” likely.
Speaking earlier today, the Environment Secretary and Brexit campaigner played down doom-mongering claims from Remainers.
He told the BBC: “I think because a deal is in all our interests, that is what the outcome will be.”
9:13pm update: Adonis’ fury at Labour’s Brexit stance
Labour peer Lord Adonis has accused his own party of being “on one long holiday” over Brexit.
Speaking in the House of Lords, the former Cabinet minister said Labour had been “largely absent from the scene” over the issue.
Lord Adonis added: “I think that the opposition has been on one long holiday for the entire period of this Brexit.
“That is part of the reason why the country is in this crisis situation at the moment.”
Labour peer Lord Adonis criticised his party’s Brexit stance
6:58pm update: NHS prepares for no-deal Brexit
Health officials are considering working with industry to stockpile drugs in the event of a no-deal Brexit.
Health Secretary Matt Hancock, a Remainer, said the Government was being “responsible” by preparing for a range of Brexit outcomes.
He told the Health Select Committee: “I have asked the department to work up options for stockpiling by industry.
“We are working with industry for the potential need for stockpiling in the event of a no-deal Brexit.”
6:07pm update: DUP’s Paisley suspended by party
Ian Paisley has been suspended by the Democratic Unionist Party.
He is one of 10 pro-Brexit Democratic Unionists helping to prop up Theresa May’s minority Government.
He was suspended by the Northern Irish party over his failure to declare two luxury family holidays paid for by the Sri Lankan government.
He could face a by-election if 10 percent of his constituents in North Antrim demand one.
Health Secretary Matt Hancock said the NHS could stockpile drugs
5:11pm update: Raab says UK can ‘thrive’ after Brexit
He told MPs: “We would have to look at the uncertainty that we would face in the short-term, but I think long-term we would still be able to thrive.
“Of course, as with all risks and opportunities, it depends how you mitigate the risks and grasp the opportunities.”
He refused to “wallow in pessimism” about the state of Brexit and vowed to give “as much energy as I can” in negotations with the EU.
4:15pm update: Brexit minister dismisses ‘scare story’
He told the House of Lords: “I am not aware of any plans for stockpiling food. It seems to me to be a fairly ridiculous scare story.
“There are many countries outside of the European Union that manage to feed their citizens perfectly satisfactorily without the benefit of EU processes.”
Ian Paisley has been suspended by the Democratic Unionist Party
3:55pm update: PM’s aide denies ‘secret plan’
The Prime Minister’s Europe adviser denied drawing up a “secret” plan for Brexit ahead of the Chequers talks.
Ex-Cabinet minister John Whittingdale said most ministers “knew nothing” of the plan until the Monday before the Chequers away day on July 6.
Asked if that was correct, Mrs May’s adviser Olly Robbins told Parliament’s Brexit Committee: “I don’t think so, no.
“The Prime Minister met a number of her colleagues over the days and weeks in the run-up to that crucial Cabinet meeting.”
2.45pm update: Corbyn slams May over ‘botched’ Brexit
Jeremy Corbyn has slammed the Government for failing business business with its “botched” Brexit plan.
Speaking the EEF manufacturers’ organisation in Birmingham, he insisted Labour could make Brexit work for manufacturers.
He said: “Theresa May and her warring Cabinet should think again, even at this late stage, and reconsider the option of negotiating a brand new customs union.”
And he claimed the UK’s trading future under the Tories would be a “nightmare” with the country “in hock to Donald Trump”.
Dominic Raab gives a Brexit update to the Exiting the EU Committee
2.06pm update: Withdrawal Bill ‘needs major surgery’
Labour’s shadow Brexit Secretary Sir Kier Starmer replied to Mr Raab’s comments by warning that the Withdrawal Bill needs “major surgery”.
He also claimed the “gimmick” of enshrining the date of March 29, 2019 in the legislation had “become unstuck”.
Sir Kier added: “We warned at the time that it wouldn’t work, and that it would need to be rubbed out.”
2.00pm update: EU law will apply after Brexit
The Withdrawal Bill will keep parts of the European Communities Act to ensure that EU law applies after Brexit, it has emerged.
Ministers will scrap the controversial European Communities Act but “save” its “effect” for the transition period.
This means EU law will continue to apply in the UK during the the 21-month transition period from March 2019 until December 2020.
Mr Raab said such a move would “provide legal certainty to businesses and individuals” before the UK quits the customs union and single market.
Jeremy Corbyn urged the Government to back his vision for a customs union
1.52pm update: Raab promises ‘smooth and orderly Brexit’
Mr Raab insisted there will be a “smooth and orderly Brexit”, despite the huge uncertainty around a deal being reached with Brussels.
He said: “This white paper is about delivering a smooth and orderly Brexit, one that respects the referendum.
“I gently say to the other side it’s not entirely clear that it’s their overriding objective of the party opposite to give effect to the referendum.
“I hope all of those who wish to see a smooth and orderly Brexit will support the Withdrawal Agreement Bill and engage seriously on the substance.”
12.30pm update: Brexit legislation passed by Holyrood ‘cannot stand’
Brexit legislation passed by the Scottish devolved administration “cannot stand”, the Supreme Court has heard.
The submission was made at the start of a challenge at the Supreme Court in London over the “competence” of the Scottish Bill.
The EU exit legislation has been referred to the court by the Attorney General and the Advocate General for Scotland.
Advocate General for Scotland Lord Keen told the court that their case was that “the Scottish Bill as a whole cannot stand”.
Brexit could cause up to 12,000 financial services jobs to leave the UK, experts warn
10.17am update: City says 12,000 financial jobs could leave UK
Brexit could cause up to 12,000 financial services jobs to move from the UK to the EU in the short term, the City of London’s policy chief has warned.
Catherine McGuinness told Parliament’s Exiting the European Union Committee: “We are not expecting a big Brexodus in the first instance.
“But depending on how things pan out in the longer term, we may see many more go.”
She said she was disappointed that the Government dropped its preferred option of future EU trade based on mutual recognition.
10.03am update: Pound continues to suffer from Brexit uncertainty
Sterling has edged above $ 1.31 but further gains for the currency were capped by continued Brexit uncertainties.
The latest updates comes after the pound slumped to a 10-month low last week.
Next week, the Bank of England could raise interest rates, with deepening economic uncertainty playing a big part.
ING FX strategist Viraj Patel warned the pound could even fall against the euro to 92p in the third quarter of the year if Brexit anxieties persist.
He added: “The price of the pound continues to reflect a fragile UK government, uncertainty over the Brexit end-state and economic policy uncertainty.”
Theresa May holds talks with the Emir of Qatar at Downing Street
9.40am update: Ministers abroad to sell May’s ‘Global Britain’ vision
Theresa May and her ministers are continuing their attempts to sell the white paper and strike new trade deals.
The Prime Minister is hosting the emir of Qatar at Downing Street for talks that will likely cover future trade with the Gulf State.
Cabinet Office minister and Mrs May’s de facto deputy David Lidington will travel to Paris for talks with French politicians.
Meanwhile, International Trade Secretary Liam Fix speak to business leaders in Washington.
8.00am update: EU Withdrawal Bill to be presented to Parliament
The EU Withdrawal Bill will be presented to Parliament amid claims Theresa May is handing a “blank cheque” to the EU.
MPs have suggested Brussels will be able to determine how much of the £39 billion divorce bill the UK will have to pay each year.
Tory MP and former Brexit Minister David Jones said the Government appeared to be “prepared to write a blank cheque” to Brussels.
But a Government spokesman said the UK would “pay no more than it owes” under the Withdrawal Agreement by appointing auditors.