Patten joins the BBC as it looks to make savings of 20% from its £3.5bn spending budget by 2017.
The broadcaster is also facing backlash about senior salaries and expenses.
The role of the BBC Trust chairman is to ensure the BBC’s editorial coverage is impartial, set top-level budgets and appoint the BBC director general.
Patten, a former Tory MP, Hong Kong governor and current Oxford University chancellor, was recommended by culture secretary Jeremy Hunt to the prime minister.
Under the terms of the BBC Royal Charter, the appointment of the BBC Trust chairman is made by the Queen on the recommendation of the prime minister.
Patten must now face a pre-appointment hearing in front of the Commons culture, media and sport select committee on 10 March, which is chaired by Tory MP John Whittingdale.
The appointment marks the return of a Tory at the head of the BBC Trust after a series of chairmen thought to be close to the Labour Party.
Patten beat off competition for the role from Sir Richard Lambert, the former director general of the CBI and former editor of the Financial Times; Dame Patricia Hodgson, the principal of Newnham College; investment banker Anthony Fry and Richard Hooper, former chairman of the Radio Authority;
Sir Michael Lyons will step down as BBC Trust chairman on 30 April.