Thundurus

After beating the Elite Four and becoming Pokemon Champion, fly to the Magnolia Town Pokemon Center and follow the path directly to the right of the building.

Then exit town from the east and start following the path south between two wooden fences.

Continue on the path until you eventually reach the eastern part of the island, where you can use Surf to continue east.

Land on the rocky island and continue on the path.

Approach the old woman in the northern part of the rocky island.

Tornadus and Thundurus will then challenge you to a double battle.

Defeating the two Pokemon stops the constant rain in the area.

Additionally, Thundurus (and Tornadus) will start roaming the world.

You can track its location using the map, and you can encounter it in the tall grass like any other wild Pokemon.