Patel, former head of revenue management, will provide financial leadership to all BBC divisions and will be in charge of the corporation's £4bn operating expenditure.
Patel joined the BBC in 1998 as group financial controller and was promoted to head of revenue management in 2001. Previously, she worked as an accountant for KPMG.
According to Smith: "I am delighted to have secured Zarin Patel for this key role at a critical time at the BBC.
"She is an outstanding leader and has brought new energy into revenue management at the BBC, reducing evasion and optimising collection costs."
Patel is one in a line of senior management changes at the BBC after a raft of departures and promotions under new director-general Mark Thompson.
Smith was promoted to chief operating office this summer, while six out of 16 key BBC executives have left since the damaging Hutton Report, excluding then director-general Greg Dyke and chairman Gavyn Davies.
Earlier this week, Dame Pauline Neville-Jones announced her resignation from the BBC board of governors -- she is one of four to resign this year.
Pic: BBC/Jonathan Knowles
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