The Forest of Dean MP and former accountant takes the role from Anne-Marie Trevelyan, who was appointed at the start of September by former prime minister Liz Truss.
Harper previously backed Sunak in his bid to become prime minister and was chief whip at the end of David Cameron’s premiership.
He also chaired the Covid Recovery Group of Conservative MPs – a group that was against lockdown restrictions – and backed the remain campaign during the 2016 EU referendum.