Is the Wii U Pro Controller compatible with the Nintendo Switch?

No.

From the Nintendo Switch FAQ:

What controllers work with Nintendo Switch?

There are multiple controller options for the Nintendo Switch console, including Joy-Con controllers and the Nintendo Switch Pro Controller. Compatible controllers will vary per game, so be sure to check game details. You can see available accessories here.

Controllers from previous Nintendo platforms are not supported.

(emphasis mine)

As noted above, the Switch has its own Pro Controller. It's more expensive than the WiiU Pro Controller, likely because it has motion controls and a Near Field Communication (NFC) reader (for Amiibo) built in.