Here’s everything you need to know about him.
Who is he?
Mr Raab – a keen Brexiter and self-declared Thatcherite – was minister for housing until he was asked to replace Mr Davis on Monday.
He is a 44-year-old Oxford-educated lawyer who, before becoming MP for Esher and Walton, in Surrey, in 2010, worked for the Foreign Office.
While MP, he also served as junior justice minister from January 2017 until January this year.
What do his colleagues say about him?
He is viewed as a potential future leader by some Conservatives and, whenever talk turns to a new generation of talent, his name is never far away.
“Highly capable, across the issues… and a pragmatist,” is how Penny Mordaunt, the international development secretary, reacted to him being named the new Brexit secretary.
Another insider described him as “a class act”, adding: “He’s very calm, very diligent, very thoughtful.”
What are his policies?
Mr Raab’s world view is detailed in a series of books he has authored and co-authored (sample title: Britannia Unchained) which read, in some parts, like a personal pitch for the top job.
He believes in “a full fat” Brexit, and has been a vocal advocate for leaving the EU since before the referendum.
As a junior minister in the Ministry of Justice, he pushed to get overseas-born prisoners serving sentences longer than a year in UK jails deported on release, while, as housing minister, he has helped implement asset-freezing policies, clamping down on undeclared money coming into London’s property market.
Have there been controversies?
Among his more surprising outbursts have been labelling feminists “obnoxious bigots” and saying men get “a raw deal” in 2011; declaring that food banks are used mainly by people with temporary cash flow problems in 2017; and suggesting, just three months ago, that immigration had pushed up housing prices “by something like 20 per cent” – a figure later questioned by the UK Statistics Authority.
Mr Raab was previously a member of a private Facebook group that called for the return of workhouses and the sale of all council homes, and previously called for Britain to use negotiations with the EU to scrap workers’ rights.
As housing minister, his department was also at the centre of scandal this year after The Daily Mirror reported that his diary secretary was selling sex on a sugar daddy website.
When the newspaper’s undercover reporter met the 20-year-old and asked about her boss, she replied: “I know everything about him” – although, as turned out that seemed mainly to refer to his lunch time habits.
“He has the same sandwich every day,” she said. “He has the same baguette with the same smoothie with a pot of fruit every day. It’s from Pret. He has the chicken Caesar and bacon baguette, superfruit pot and the vitamin volcano smoothie.”
How will he take to the new role?
His first task may well be attempting to reset personal relations with the EU’s chief negotiator, Michel Barnier. In September last year, Mr Raab accused his now main interlocutor of being “unprofessional” after the Frenchman said he wanted to “teach” the UK a lesson.
Being able to smooth such grievances while getting to grips with the complexities on a uniquely difficult posting will be key if he is to make a success of what is being called an impossible job.
Anything else to know?
He’s a married father-of-two with a black belt in karate.