Ms McVey was named in the role late last night, which will also see her attend cabinet.
It came just after Robert Jenrick was named as secretary of state for housing, communities and local government.
Number 10 said that the portfolios for ministers were still yet to be firmed up and could not confirm exactly what Ms McVey’s role would be.
It is also unclear what position current housing minister Kit Malthouse will take on. Mr Malthouse made a bid to become leader of the Conservative Party before dropping out of the race.
Ms McVey, 51, also bid for the leadership but came in last place.