The appointment was part of a cabinet reshuffle by Prime Minister David Cameron over the past few days.
Mr Davies was executive chairman of the FSA from 1997-2003, joining as the first chairman of the then new financial regulator.
He also worked as deputy governor of the Bank of England from 1995-1997.
Within his role on the future committee, he will be responsible for examining airport capacity both at Heathrow and at a proposed airport in East London.

Former Transport Secretary Justine Greening, a strong opponent of Heathrow expansion, has been moved to Secretary of State for International Development.
An interim report on his findings will be published in 2013 although there will be no formal report until 2015.
Other changes include Mark Hoban MP, former financial secretary to the Treasury, moving to become Employment Minister within the Department for Work and Pensions.
His replacement will be Greg Clark, formerly Minister for Cities and Decentralisation and Planning.
This meant he did not give evidence to the Treasury Select Committee today as he had been due to do, his replacement will attend in a week's time.
Iain Duncan Smith remains secretary for work and pensions as does Steve Webb in his position as Pensions Minister.