The proposal was passed with a 39 to none vote in favour of abolishing prescription charges, but the Conservatives and Liberal Democrats chose to abstain.
Drug manufacturers have warned that removing a prescription charge will lead to waste and reduced funding for new medicines. However, Welsh Health Minister Brian Gibbons said that free prescriptions will ensure that people are not put off getting medicines just because of the cost.
The scheme is expected to cost £29.5m in the first year.
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