A water park at Llys y Fran Water Park, a regeneration project in Saundersfoot and a railway museum in Aberystwyth are among the plans which could benefit.
The Welsh Government said the potential value - if other public and private funding is secured - would be £85m.
It said it was the single biggest EU investment in the sector, with cash stretching over five years.
Ten projects have been picked and will now be individually assessed and agreed before building work can start.
They are:
Economy Minister Edwina Hart said: "This announcement brings us one step closer to creating some iconic destinations for Wales.
"By focusing efforts and investment on key projects in each region we can have a real impact on Wales' profile in this globally competitive market."
Ten projects to boost tourism across Wales could receive £27.7m in European funding.