He has replaced Alok Sharma, who was in the role for just seven months and has become employment minister in the Department for Work and Pensions.
Meanwhile, the Department for Communities and Local Government and the secretary of state post have been renamed.
Sajid Javid’s job title has been changed to include housing. It is now the secretary of state for housing, communities and local government, and comes as the government targets the delivery of 300,000 homes per year by the mid-2020s.
The Department for Communities and Local Government is being renamed the Ministry of Housing, Communities and Local Government (MHCLG).
Mr Javid said: “Building the homes our country needs is an absolute priority for this government and so I’m delighted the prime minister has asked me to serve in this role.
“The name change for the department reflects this government’s renewed focus to deliver more homes and build strong communities across England.”
Mr Raab, who becomes the seventh housing minister since 2010, tweeted: “I have thoroughly enjoyed working at MoJ on court reform, my thanks to the team there... and I’m looking forward to getting stuck into the housing brief, vital to building the new homes we need.”
In other changes following prime minister Theresa May’s January 2018 reshuffle, Esther McVey has become secretary of state for work and pensions replacing David Gauke, who has moved to justice secretary. She will oversee the continuing roll-out of Universal Credit.
Terrie Alafat, chief executive of the Chartered Institute of Housing (CIH), said she hopes “the very valuable work Alok Sharma has been doing, including his work travelling around the country to consult with tenants, continues”.
“Given the very serious housing challenges our nation faces we also now hope for continuity in this crucial role,” she added.
David Orr, chief executive of the National Housing Federation, said he hopes the appointment “will bring some continuity and stability to the challenge of ending the housing crisis”.
He said Mr Sharma had “achieved many great things in just seven months, including the increased £2bn funding for affordable homes”.
“Housing needs to remain a priority for this government and housing associations will continue to be constructive and vital partners for them.”
The National Federation of Builders called for the government to end the high turnover of housing ministers.