The petition has been launched by the National Union of Journalists (NUJ) and the Broadcasting Entertainment Cinematograph and Theatre Union (BECTU).
The petition follows an early day motion on the subject moved in the House of Commons earlier this month by George Galloway, MP, and supported by several others.
The petition calls upon the BBC to halt its plans to off-shore jobs and programmes in the World Service and deplores the fact that there has been no proper consultation with staff and their trade unions.
It says "We deplore that there has been no opportunity for staff at Bush House to contribute to a dynamic plan for the development of the BBC's international broadcasting activities. We believe that the employment conditions being offered exploit journalists in developing nations, and may not give proper protection for their safety, and that the BBC is surreptitiously dismantling the World Service in a way that may damage its editorial credibility."
Defending the plans to move staff to their countries of origin in south Asia, the BBC said it had plans to have around 50 per cent of overall language service staff located closer to their audiences.
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Mike Gardner, Head of Media Relations at the BBC World Service, told PTI that the BBC management was in discussions with staff and unions about the changes.
He said "The proposed redeployments of staff to India, Pakistan and Nepal recognise the new media realities in those countries. It has been BBC World Service's policy for its language services to be working closer to the audiences they serve for some time."