Most staff cuts will be within human resources, communications and administration. The job cuts will save £320 million over three years which will be reinvested in news and original programming.
Mr Thompson also announced that several departments, including new media, will be moved to a new BBC centre in Manchester.
"My vision for the future of the BBC has three parts: a bold new programme and content strategy based above all around the idea of excellence; a transformation of the BBC into a state-of-the art digital broadcaster; and an irreversible shift in the culture of the BBC towards simplicity, opportunity and creativity," said Mr Thompson.
"We should do what's right for a strong, independent BBC and its audiences in the long term, not what's politically convenient now."
The public is invited to comment on the plans through the BBC website.
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