Hancock takes over from Michael Fallon as business and energy minister with construction part of his remit.
He will attend cabinet meetings as part of his new role while Fallon has been promoted to defence secretary.
In other moves Michael Gove has been replaced as education secretary by Nicky Morgan while Greg Barker is replaced as energy minister by Amber Rudd.
Planning minister Nick Boles will take over Hancock’s former brief as business and education minister with the planning role likely to go to Penny Mordaunt.
Stephen Hammond has been replaced as transport minister by John Hayes.