Robertson, who helped oversee London’s staging of the 2012 Olympic Games during his three-year term, has been promoted to the foreign office as minister of state.
Grant, 52, is a former junior judo champion and qualified solicitor. She had worked at the Ministry of Justice and will now assume her new role alongside the additional duties of equalities minister.
High on Grant’s remit will be the ongoing task of ensuring a legacy from the 2012 Games.
UK Sport chairman Rod Carr said: “We look forward to working closely with Helen Grant as we move towards the Winter Olympics and Rio 2016.”