Robbie and Lynch will join Robert Webb QC, general counsel at British Airways, and Dr Samir Shah, chief executive of independent production company Juniper Communications, who will begin their appointments on January 1.
The appointments are in response to changes of governance at the corporation, which have been set out by the BBC's new charter and agreement.
Part of these changes include the BBC Trust replacing the BBC Board of Governors on January 1, with eight new members, including David Liddiment, former director of programmes at ITV, and Patricia Hodgson, former chief executive of the Independent Television Commission.
The creation of the trust was outlined in the government's BBC Charter white paper in March, and members will be responsible for ensuring the corporation fulfils its public service broadcasting remit.
The corporation said that one further non-executive director would be named early next year, following the appointment of Marcus Agius, chairman designate of Barclays Bank, who was made senior independent director last month.
Mark Thompson, BBC director-general, said: "This is an important moment in a new system of running the BBC under the new charter and agreement.
"Together, they bring an exceptional range of skills, experience and perspectives which I believe will be crucial in our decision-making process as we seek to deliver a very challenging agenda in the years ahead."
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