The policy was part of the co-operation deal signed between Labour and Plaid Cymru in 2021.
Conservatives have said it will risk jobs in the tourism industry, which employs 159,000 people - nearly 12% of Wales' workforce.
In a report last year, MPs on the Commons Welsh Affairs Committee said they were concerned it could deter international tourists.
But Finance Secretary Mark Drakeford said it was "fair visitors contribute towards local facilities, helping to fund infrastructure and services integral to their experience".
He added: "Visitor levies are common around the world, benefiting local communities, tourists and businesses - and we want the same for Wales."
Anyone providing accommodation, including owners of short-term accommodation such as Airbnbs, will have to register under the law creating the tax.
Eventually, they will need a licence to operate to make sure they all follow the same rules and safety standards.
More legislation to create the licensing scheme is expected before the next Senedd election in 2026.