The Conservative MP was elected to replace Dame Meg Hillier, who was recently named as chair of the influential Treasury Committee.
The Public Accounts Committee, which is always chaired by a member of the official opposition, holds regular hearings with senior officials from HMRC so current service levels are likely to be high on the agenda when parliament returns to committee sessions after the party conference break.
Members of the committee will be confirmed in due course.
Following the election result, Sir Geoffrey said: ‘I am honoured to have been elected chair of the Public Accounts Committee. I am very grateful to all my colleagues for their support.
‘I would like to thank in particular the previous PAC chair Dame Meg Hillier, both for her endorsement of my candidacy and for her steadfast leadership of the previous Committee.