The prime minister had already confirmed on Friday, soon after the general election results were confirmed, that five of her top-most Cabinet posts will remain unchanged - including Philip Hammond as chancellor of the exchequer, Amber Rudd as home secretary, Boris Johnson as foreign secretary, David Davis as Brexit secretary and Michael Fallon in charge of the ministry of defence.
May and Green - who backed Remain in the Brexit referendum - have known each other since they were Oxford students together in the 1970s and he is considered one of her few close allies.
In other early appointments, Greg Clark holds on to his job as secretary of state for business, energy and industrial strategy and David Gauke takes over as work and pensions minister.
Far from a forecast landslide majority, May has been left holding on to 10 Downing Street with diminished authority - having lost her party its majority.