Labour Assembly Members, which previously rejected the idea, supported the motion championed by Plaid Cymru. AMs voted 38 to 10 in favour, with no members abstaining.
The vote proposed bringing forward plans to use new taxation powers under the Wales Act 2014 to allow the next Welsh government to introduce a levy on sugary drinks.
Elin Jones, Plaid’s shadow health minister, said: “Excess sugar consumption is one of the biggest risks to public health and unless we take action the threat will continue to grow.
"I'm pleased that the Welsh government has today U-turned and supported our proposals."
Research by Plaid Cymru has suggested introducing a tax on sugary drinks could cut the number of obese people in Wales by 8,300 and those overweight by 13,300.
There have been numerous calls by senior MPs and health bodies for the UK government to introduce a similar levy.