The MPS said that following 'extensive negotiations' it had agreed the transfer with the Welsh government.
State-backed GP indemnity took effect from 1 April 2019 across England and Wales for 'future liabilities' - claims relating to events that occurred after that date.
The transfer of existing liabilities - responsibility for claims arising for incidents that occurred before 1 April 2019 - has proven far more complex.
In England, both the MPS and the MDDUS have now agreed the transfer - meaning GPs indemnified through these organisations have now fully switched to the state-backed indemnity system.
The MDU, however - which estimates it represents 47% of English GPs - is locked in a legal battle over the transfer of existing liabilities. The MDU admitted last month that the lack of a deal with the UK government had left it facing 'increased demand' for payouts 'against dwindling funds'.
In Wales, a framework for the transfer of existing liabilities was not in place when state-backed indemnity began in April, but the MPS has now become the first medico-legal organisation to secure a deal. The MDDUS said last month it was 'in discussions' with the Welsh government over the transfer and could be set to follow suit.
The MDU, however, is also in a legal dispute with the Welsh government over the issue. In evidence provided to a Welsh parliamentary committee the MDU said that after 1 April it had 'continued to try to find a solution with the Welsh government but, regrettably, as no agreement was reached and our GP members are left with their historic liabilities, the MDU had to resort to judicial review proceedings which remain pending'.
MPS executive director Howard Kew said: 'This is a positive outcome for MPS general practice members in Wales – it means they will benefit from a similar approach that was taken for hospital doctors when their arrangements were introduced in 1990, and is something we have argued for ever since proposals for state-backed indemnity were announced. We have reached this agreement following constructive and collaborative discussions with the Welsh government.
'I am pleased that our general practice members in both England and Wales are now able to turn to a government backed scheme for help no matter when in the future they become aware of a claim against them.
'To ensure a smooth transition, MPS will continue to manage existing claims for GPs in Wales during an interim period. After this time, claims will be managed by NHS Wales Shared Services Partnership, which has extensive experience of managing clinical negligence claims on behalf of health boards.'
A Welsh government spokesperson said: 'We are very pleased to have reached agreement with the MPS. Discussions with the MDDUS and MDU are ongoing. The minister for health and social services intends to reach an existing liabilities scheme agreement with all three established MDOs, subject to the conclusion of legal and financial due diligence and satisfactory discussions.'